define representation data

Graphical Representation of Data

Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables. Graphical representation of data is done through different mediums such as lines, plots, diagrams, etc. Let us learn more about this interesting concept of graphical representation of data, the different types, and solve a few examples.

Definition of Graphical Representation of Data

A graphical representation is a visual representation of data statistics-based results using graphs, plots, and charts. This kind of representation is more effective in understanding and comparing data than seen in a tabular form. Graphical representation helps to qualify, sort, and present data in a method that is simple to understand for a larger audience. Graphs enable in studying the cause and effect relationship between two variables through both time series and frequency distribution. The data that is obtained from different surveying is infused into a graphical representation by the use of some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. This visual representation helps in clarity, comparison, and understanding of numerical data.

Representation of Data

The word data is from the Latin word Datum, which means something given. The numerical figures collected through a survey are called data and can be represented in two forms - tabular form and visual form through graphs. Once the data is collected through constant observations, it is arranged, summarized, and classified to finally represented in the form of a graph. There are two kinds of data - quantitative and qualitative. Quantitative data is more structured, continuous, and discrete with statistical data whereas qualitative is unstructured where the data cannot be analyzed.

Principles of Graphical Representation of Data

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin. On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value. When -axis and y-axis intersect each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV. This form of representation is seen in a frequency distribution that is represented in four methods, namely Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

Advantages and Disadvantages of Graphical Representation of Data

Listed below are some advantages and disadvantages of using a graphical representation of data:

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.
• It is mainly used in statistics to determine the mean, median, and mode for different data

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represent it graphically.

Rules of Graphical Representation of Data

While presenting data graphically, there are certain rules that need to be followed. They are listed below:

• Suitable Title: The title of the graph should be appropriate that indicate the subject of the presentation.
• Measurement Unit: The measurement unit in the graph should be mentioned.
• Proper Scale: A proper scale needs to be chosen to represent the data accurately.
• Index: For better understanding, index the appropriate colors, shades, lines, designs in the graphs.
• Data Sources: Data should be included wherever it is necessary at the bottom of the graph.
• Simple: The construction of a graph should be easily understood.
• Neat: The graph should be visually neat in terms of size and font to read the data accurately.

Uses of Graphical Representation of Data

The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data. It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision. The visual display of data also helps in avoiding confusion and overlapping of any information. Graphs like line graphs and bar graphs, display two or more data clearly for easy comparison. This is important in communicating our findings to others and our understanding and analysis of the data.

Types of Graphical Representation of Data

Data is represented in different types of graphs such as plots, pies, diagrams, etc. They are as follows,

Related Topics

Listed below are a few interesting topics that are related to the graphical representation of data, take a look.

• x and y graph
• Frequency Polygon
• Cumulative Frequency

Examples on Graphical Representation of Data

Example 1 : A pie chart is divided into 3 parts with the angles measuring as 2x, 8x, and 10x respectively. Find the value of x in degrees.

We know, the sum of all angles in a pie chart would give 360º as result. ⇒ 2x + 8x + 10x = 360º ⇒ 20 x = 360º ⇒ x = 360º/20 ⇒ x = 18º Therefore, the value of x is 18º.

Example 2: Ben is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions? i) What is the mode of the plot? ii) What is the mean of the plot? iii) Find the range.

Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.

Hence, mode = 54

ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958

To find the mean, we have to divide the sum by the total number of values.

Mean = Sum of all data values ÷ 19 = 958 ÷ 19 = 50.42

iii) Range = the highest value - the lowest value = 91 - 12 = 79

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Practice Questions on Graphical Representation of Data

Faqs on graphical representation of data, what is graphical representation.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

• Stem and leaf plot
• Scatter diagrams
• Frequency Distribution

Is the Graphical Representation of Numerical Data?

Yes, these graphical representations are numerical data that has been accumulated through various surveys and observations. The method of presenting these numerical data is called a chart. There are different kinds of charts such as a pie chart, bar graph, line graph, etc, that help in clearly showcasing the data.

What is the Use of Graphical Representation of Data?

Graphical representation of data is useful in clarifying, interpreting, and analyzing data plotting points and drawing line segments , surfaces, and other geometric forms or symbols.

What are the Ways to Represent Data?

Tables, charts, and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organization, and analysis of data as part of the process of a scientific study.

What is the Objective of Graphical Representation of Data?

The main objective of representing data graphically is to display information visually that helps in understanding the information efficiently, clearly, and accurately. This is important to communicate the findings as well as analyze the data.

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2.1: Types of Data Representation

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Two common types of graphic displays are bar charts and histograms. Both bar charts and histograms use vertical or horizontal bars to represent the number of data points in each category or interval. The main difference graphically is that in a  bar chart  there are spaces between the bars and in a  histogram  there are not spaces between the bars. Why does this subtle difference exist and what does it imply about graphic displays in general?

Displaying Data

It is often easier for people to interpret relative sizes of data when that data is displayed graphically. Note that a  categorical variable  is a variable that can take on one of a limited number of values and a  quantitative variable  is a variable that takes on numerical values that represent a measurable quantity. Examples of categorical variables are tv stations, the state someone lives in, and eye color while examples of quantitative variables are the height of students or the population of a city. There are a few common ways of displaying data graphically that you should be familiar with. 

A  pie chart  shows the relative proportions of data in different categories.  Pie charts  are excellent ways of displaying categorical data with easily separable groups. The following pie chart shows six categories labeled A−F.  The size of each pie slice is determined by the central angle. Since there are 360 o  in a circle, the size of the central angle θ A  of category A can be found by:

CK-12 Foundation -  https://www.flickr.com/photos/slgc/16173880801  - CCSA

A  bar chart  displays frequencies of categories of data. The bar chart below has 5 categories, and shows the TV channel preferences for 53 adults. The horizontal axis could have also been labeled News, Sports, Local News, Comedy, Action Movies. The reason why the bars are separated by spaces is to emphasize the fact that they are categories and not continuous numbers. For example, just because you split your time between channel 8 and channel 44 does not mean on average you watch channel 26. Categories can be numbers so you need to be very careful.

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A  histogram  displays frequencies of quantitative data that has been sorted into intervals. The following is a histogram that shows the heights of a class of 53 students. Notice the largest category is 56-60 inches with 18 people.

A  boxplot  (also known as a  box and whiskers plot ) is another way to display quantitative data. It displays the five 5 number summary (minimum, Q1,  median , Q3, maximum). The box can either be vertically or horizontally displayed depending on the labeling of the axis. The box does not need to be perfectly symmetrical because it represents data that might not be perfectly symmetrical.

Earlier, you were asked about the difference between histograms and bar charts. The reason for the space in bar charts but no space in histograms is bar charts graph categorical variables while histograms graph quantitative variables. It would be extremely improper to forget the space with bar charts because you would run the risk of implying a spectrum from one side of the chart to the other. Note that in the bar chart where TV stations where shown, the station numbers were not listed horizontally in order by size. This was to emphasize the fact that the stations were categories.

Create a boxplot of the following numbers in your calculator.

8.5, 10.9, 9.1, 7.5, 7.2, 6, 2.3, 5.5

Enter the data into L1 by going into the Stat menu.

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Then turn the statplot on and choose boxplot.

Use Zoomstat to automatically center the window on the boxplot.

Create a pie chart to represent the preferences of 43 hungry students.

• Other – 5
• Burritos – 7
• Burgers – 9
• Pizza – 22

Create a bar chart representing the preference for sports of a group of 23 people.

• Football – 12
• Baseball – 10
• Basketball – 8
• Hockey – 3

Create a histogram for the income distribution of 200 million people.

• Below $50,000 is 100 million people
• Between $50,000 and $100,000 is 50 million people
• Between $100,000 and $150,000 is 40 million people
• Above $150,000 is 10 million people

1. What types of graphs show categorical data?

2. What types of graphs show quantitative data?

A math class of 30 students had the following grades:

3. Create a bar chart for this data.

4. Create a pie chart for this data.

5. Which graph do you think makes a better visual representation of the data?

A set of 20 exam scores is 67, 94, 88, 76, 85, 93, 55, 87, 80, 81, 80, 61, 90, 84, 75, 93, 75, 68, 100, 98

6. Create a histogram for this data. Use your best judgment to decide what the intervals should be.

7. Find the  five number summary  for this data.

8. Use the  five number summary  to create a boxplot for this data.

9. Describe the data shown in the boxplot below.

10. Describe the data shown in the histogram below.

A math class of 30 students has the following eye colors:

11. Create a bar chart for this data.

12. Create a pie chart for this data.

13. Which graph do you think makes a better visual representation of the data?

14. Suppose you have data that shows the breakdown of registered republicans by state. What types of graphs could you use to display this data?

15. From which types of graphs could you obtain information about the spread of the data? Note that spread is a measure of how spread out all of the data is.

Review (Answers)

To see the Review answers, open this  PDF file  and look for section 15.4. 

Additional Resources

PLIX: Play, Learn, Interact, eXplore - Baby Due Date Histogram

Practice: Types of Data Representation

Real World: Prepare for Impact

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2: Graphical Representations of Data

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In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.

• 2.1: Introduction In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs. Our emphasis will be on histograms and box plots.
• 2.2: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs A stem-and-leaf plot is a way to plot data and look at the distribution, where all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends.  A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories.
• 2.3: Histograms, Frequency Polygons, and Time Series Graphs A histogram is a graphic version of a frequency distribution. The graph consists of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Histograms are typically used for large, continuous, quantitative data sets. A frequency polygon can also be used when graphing large data sets with data points that repeat.
• 2.4: Using Excel to Create Graphs Using technology to create graphs will make the graphs faster to create, more precise, and give the ability to use larger amounts of data. This section focuses on using Excel to create graphs.
• 2.5: Graphs that Deceive It's common to see graphs displayed in a misleading manner in social media and other instances. This could be done purposefully to make a point, or it could be accidental. Either way, it's important to recognize these instances to ensure you are not misled.
• 2.E: Graphical Representations of Data (Exercises) These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

Contributors and Attributions

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .

What Is Data Visualization: Brief Theory, Useful Tips and Awesome Examples

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By Al Boicheva

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Updated: June 23, 2022

To create data visualization in order to present your data is no longer just a nice to have skill. Now, the skill to effectively sort and communicate your data through charts is a must-have for any business in any field that deals with data. Data visualization helps businesses quickly make sense of complex data and start making decisions based on that data. This is why today we’ll talk about what is data visualization. We’ll discuss how and why does it work, what type of charts to choose in what cases, how to create effective charts, and, of course, end with beautiful examples.

So let’s jump right in. As usual, don’t hesitate to fast-travel to a particular section of your interest.

Article overview: 1. What Does Data Visualization Mean? 2. How Does it Work? 3. When to Use it? 4. Why Use it? 5. Types of Data Visualization 6. Data Visualization VS Infographics: 5 Main Differences 7. How to Create Effective Data Visualization?: 5 Useful Tips 8. Examples of Data Visualization

1. What is Data Visualization?

Data Visualization is a graphic representation of data that aims to communicate numerous heavy data in an efficient way that is easier to grasp and understand . In a way, data visualization is the mapping between the original data and graphic elements that determine how the attributes of these elements vary. The visualization is usually made by the use of charts, lines, or points, bars, and maps.

• Data Viz is a branch of Descriptive statistics but it requires both design, computer, and statistical skills.
• Aesthetics and functionality go hand in hand to communicate complex statistics in an intuitive way.
• Data Viz tools and technologies are essential for making data-driven decisions.
• It’s a fine balance between form and functionality.
• Every STEM field benefits from understanding data.

2. How Does it Work?

If we can see it, our brains can internalize and reflect on it. This is why it’s much easier and more effective to make sense of a chart and see trends than to read a massive document that would take a lot of time and focus to rationalize. We wouldn’t want to repeat the cliche that humans are visual creatures, but it’s a fact that visualization is much more effective and comprehensive.

In a way, we can say that data Viz is a form of storytelling with the purpose to help us make decisions based on data. Such data might include:

• Tracking sales
• Identifying trends
• Identifying changes
• Monitoring goals
• Monitoring results
• Combining data

3. When to Use it?

Data visualization is useful for companies that deal with lots of data on a daily basis. It’s essential to have your data and trends instantly visible. Better than scrolling through colossal spreadsheets. When the trends stand out instantly this also helps your clients or viewers to understand them instead of getting lost in the clutter of numbers.

With that being said, Data Viz is suitable for:

• Annual reports
• Presentations
• Social media micronarratives
• Informational brochures
• Trend-trafficking
• Candlestick chart for financial analysis
• Determining routes

Common cases when data visualization sees use are in sales, marketing, healthcare, science, finances, politics, and logistics.

4. Why Use it?

Short answer: decision making. Data Visualization comes with the undeniable benefits of quickly recognizing patterns and interpret data. More specifically, it is an invaluable tool to determine the following cases.

• Identifying correlations between the relationship of variables.
• Getting market insights about audience behavior.
• Determining value vs risk metrics.
• Monitoring trends over time.
• Examining rates and potential through frequency.
• Ability to react to changes.

5. Types of Data Visualization

As you probably already guessed, Data Viz is much more than simple pie charts and graphs styled in a visually appealing way. The methods that this branch uses to visualize statistics include a series of effective types.

Map visualization is a great method to analyze and display geographically related information and present it accurately via maps. This intuitive way aims to distribute data by region. Since maps can be 2D or 3D, static or dynamic, there are numerous combinations one can use in order to create a Data Viz map.

COVID-19 Spending Data Visualization POGO by George Railean

The most common ones, however, are:

• Regional Maps: Classic maps that display countries, cities, or districts. They often represent data in different colors for different characteristics in each region.
• Line Maps: They usually contain space and time and are ideal for routing, especially for driving or taxi routes in the area due to their analysis of specific scenes.
• Point Maps: These maps distribute data of geographic information. They are ideal for businesses to pinpoint the exact locations of their buildings in a region.
• Heat Maps: They indicate the weight of a geographical area based on a specific property. For example, a heat map may distribute the saturation of infected people by area.

Charts present data in the form of graphs, diagrams, and tables. They are often confused with graphs since graphs are indeed a subcategory of charts. However, there is a small difference: graphs show the mathematical relationship between groups of data and is only one of the chart methods to represent data.

Infographic Data Visualization by Madeline VanRemmen

With that out of the way, let’s talk about the most basic types of charts in data visualization.

They use a series of bars that illustrate data development.  They are ideal for lighter data and follow trends of no more than three variables or else, the bars become cluttered and hard to comprehend. Ideal for year-on-year comparisons and monthly breakdowns.

These familiar circular graphs divide data into portions. The bigger the slice, the bigger the portion. They are ideal for depicting sections of a whole and their sum must always be 100%. Avoid pie charts when you need to show data development over time or lack a value for any of the portions. Doughnut charts have the same use as pie charts.

They use a line or more than one lines that show development over time. It allows tracking multiple variables at the same time. A great example is tracking product sales by a brand over the years. Area charts have the same use as line charts.

Scatter Plot

These charts allow you to see patterns through data visualization. They have an x-axis and a y-axis for two different values. For example, if your x-axis contains information about car prices while the y-axis is about salaries, the positive or negative relationship will tell you about what a person’s car tells about their salary.

Unlike the charts we just discussed, tables show data in almost a raw format. They are ideal when your data is hard to present visually and aim to show specific numerical data that one is supposed to read rather than visualize.

Data Visualisation | To bee or not to bee by Aishwarya Anand Singh

For example, charts are perfect to display data about a particular illness over a time period in a particular area, but a table comes to better use when you also need to understand specifics such as causes, outcomes, relapses, a period of treatment, and so on.

6. Data Visualization VS Infographics

5 main differences.

They are not that different as both visually represent data. It is often you search for infographics and find images titled Data Visualization and the other way around. In many cases, however, these titles aren’t misleading. Why is that?

• Data visualization is made of just one element. It could be a map, a chart, or a table. Infographics , on the other hand, often include multiple Data Viz elements.
• Unlike data visualizations that can be simple or extremely complex and heavy, infographics are simple and target wider audiences. The latter is usually comprehensible even to people outside of the field of research the infographic represents.
• Interestingly enough, data Viz doesn’t offer narratives and conclusions, it’s a tool and basis for reaching those. While infographics, in most cases offer a story and a narrative. For example, a data visualization map may have the title “Air pollution saturation by region”, while an infographic with the same data would go “Areas A and B are the most polluted in Country C”.
• Data visualizations can be made in Excel or use other tools that automatically generate the design unless they are set for presentation or publishing. The aesthetics of infographics , however, are of great importance and the designs must be appealing to wider audiences.
• In terms of interaction, data visualizations often offer interactive charts, especially in an online form. Infographics, on the other hand, rarely have interaction and are usually static images.

While on topic, you could also be interested to check out these 50 engaging infographic examples that make complex data look great.

7. Tips to Create Effective Data Visualization

The process is naturally similar to creating Infographics and it revolves around understanding your data and audience. To be more precise, these are the main steps and best practices when it comes to preparing an effective visualization of data for your viewers to instantly understand.

1. Do Your Homework

Preparation is half the work already done. Before you even start visualizing data, you have to be sure you understand that data to the last detail.

Knowing your audience is undeniable another important part of the homework, as different audiences process information differently. Who are the people you’re visualizing data for? How do they process visual data? Is it enough to hand them a single pie chart or you’ll need a more in-depth visual report?

The third part of preparing is to determine exactly what you want to communicate to the audience. What kind of information you’re visualizing and does it reflect your goal?

And last, think about how much data you’ll be working with and take it into account.

2. Choose the Right Type of Chart

In a previous section, we listed the basic chart types that find use in data visualization. To determine best which one suits your work, there are a few things to consider.

• How many variables will you have in a chart?
• How many items will you place for each of your variables?
• What will be the relation between the values (time period, comparison, distributions, etc.)

With that being said, a pie chart would be ideal if you need to present what portions of a whole takes each item. For example, you can use it to showcase what percent of the market share takes a particular product. Pie charts, however, are unsuitable for distributions, comparisons, and following trends through time periods. Bar graphs, scatter plots,s and line graphs are much more effective in those cases.

Another example is how to use time in your charts. It’s way more accurate to use a horizontal axis because time should run left to right. It’s way more visually intuitive.

3. Sort your Data

Start with removing every piece of data that does not add value and is basically excess for the chart. Sometimes, you have to work with a huge amount of data which will inevitably make your chart pretty complex and hard to read. Don’t hesitate to split your information into two or more charts. If that won’t work for you, you could use highlights or change the entire type of chart with something that would fit better.

Tip: When you use bar charts and columns for comparison, sort the information in an ascending or a descending way by value instead of alphabetical order.

4. Use Colors to Your Advantage

In every form of visualization, colors are your best friend and the most powerful tool. They create contrasts, accents, and emphasis and lead the eye intuitively. Even here, color theory is important.

When you design your chart, make sure you don’t use more than 5 or 6 colors. Anything more than that will make your graph overwhelming and hard to read for your viewers. However, color intensity is a different thing that you can use to your advantage. For example, when you compare the same concept in different periods of time, you could sort your data from the lightest shade of your chosen color to its darker one. It creates a strong visual progression, proper to your timeline.

Things to consider when you choose colors:

• Different colors for different categories.
• A consistent color palette for all charts in a series that you will later compare.
• It’s appropriate to use color blind-friendly palettes.

5. Get Inspired

Always put your inspiration to work when you want to be at the top of your game. Look through examples, infographics, and other people’s work and see what works best for each type of data you need to implement.

This Twitter account Data Visualization Society is a great way to start. In the meantime, we’ll also handpick some amazing examples that will get you in the mood to start creating the visuals for your data.

8. Examples for Data Visualization

As another art form, Data Viz is a fertile ground for some amazing well-designed graphs that prove that data is beautiful. Now let’s check out some.

Dark Souls III Experience Data

We start with Meng Hsiao Wei’s personal project presenting his experience with playing Dark Souls 3. It’s a perfect example that infographics and data visualization are tools for personal designs as well. The research is pretty massive yet very professionally sorted into different types of charts for the different concepts. All data visualizations are made with the same color palette and look great in infographics.

My dark souls 3 playing data by Meng Hsiao Wei

Greatest Movies of all Time

Katie Silver has compiled a list of the 100 greatest movies of all time based on critics and crowd reviews. The visualization shows key data points for every movie such as year of release, oscar nominations and wins, budget, gross, IMDB score, genre, filming location, setting of the film, and production studio. All movies are ordered by the release date.

100 Greatest Movies Data Visualization by Katie Silver

The Most Violent Cities

Federica Fragapane shows data for the 50 most violent cities in the world in 2017. The items are arranged on a vertical axis based on population and ordered along the horizontal axis according to the homicide rate.

The Most Violent Cities by Federica Fragapane

Family Businesses as Data

These data visualizations and illustrations were made by Valerio Pellegrini for Perspectives Magazine. They show a pie chart with sector breakdown as well as a scatter plot for contribution for employment.

PERSPECTIVES MAGAZINE – Family Businesses by Valerio Pellegrini

Orbit Map of the Solar System

The map shows data on the orbits of more than 18000 asteroids in the solar system. Each asteroid is shown at its position on New Years’ Eve 1999, colored by type of asteroid.

An Orbit Map of the Solar System by Eleanor Lutz

The Semantics Of Headlines

Katja Flükiger has a take on how headlines tell the story. The data visualization aims to communicate how much is the selling influencing the telling. The project was completed at Maryland Institute College of Art to visualize references to immigration and color-coding the value judgments implied by word choice and context.

The Semantics of Headlines by Katja Flükiger

Moon and Earthquakes

This data visualization works on answering whether the moon is responsible for earthquakes. The chart features the time and intensity of earthquakes in response to the phase and orbit location of the moon.

Moon and Earthquakes by Aishwarya Anand Singh

Dawn of the Nanosats

The visualization shows the satellites launched from 2003 to 2015. The graph represents the type of institutions focused on projects as well as the nations that financed them. On the left, it is shown the number of launches per year and satellite applications.

WIRED UK – Dawn of the by Nanosats by Valerio Pellegrini

Final Words

Data visualization is not only a form of science but also a form of art. Its purpose is to help businesses in any field quickly make sense of complex data and start making decisions based on that data. To make your graphs efficient and easy to read, it’s all about knowing your data and audience. This way you’ll be able to choose the right type of chart and use visual techniques to your advantage.

You may also be interested in some of these related articles:

• Infographics for Marketing: How to Grab and Hold the Attention
• 12 Animated Infographics That Will Engage Your Mind from Start to Finish
• 50 Engaging Infographic Examples That Make Complex Ideas Look Great
• Good Color Combinations That Go Beyond Trends: Inspirational Examples and Ideas

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Data Representation

Literature on data representation.

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Data Representation in Computer: Number Systems, Characters, Audio, Image and Video

• by Anuj Kumar
• 16 July 2021 16 February 2024
• Computer Science

Table of Contents

• 1 What is Data Representation in Computer?
• 2.1 Binary Number System
• 2.2 Octal Number System
• 2.3 Decimal Number System
• 2.4 Hexadecimal Number System
• 3.4 Unicode
• 4 Data Representation of Audio, Image and Video
• 5.1 What is number system with example?

What is Data Representation in Computer?

A computer uses a fixed number of bits to represent a piece of data which could be a number, a character, image, sound, video, etc. Data representation is the method used internally to represent data in a computer. Let us see how various types of data can be represented in computer memory.

Before discussing data representation of numbers, let us see what a number system is.

Number Systems

Number systems are the technique to represent numbers in the computer system architecture, every value that you are saving or getting into/from computer memory has a defined number system.

A number is a mathematical object used to count, label, and measure. A number system is a systematic way to represent numbers. The number system we use in our day-to-day life is the decimal number system that uses 10 symbols or digits.

The number 289 is pronounced as two hundred and eighty-nine and it consists of the symbols 2, 8, and 9. Similarly, there are other number systems. Each has its own symbols and method for constructing a number.

A number system has a unique base, which depends upon the number of symbols. The number of symbols used in a number system is called the base or radix of a number system.

Let us discuss some of the number systems. Computer architecture supports the following number of systems:

Binary Number System

Octal number system, decimal number system, hexadecimal number system.

A Binary number system has only two digits that are 0 and 1. Every number (value) represents 0 and 1 in this number system. The base of the binary number system is 2 because it has only two digits.

The octal number system has only eight (8) digits from 0 to 7. Every number (value) represents with 0,1,2,3,4,5,6 and 7 in this number system. The base of the octal number system is 8, because it has only 8 digits.

The decimal number system has only ten (10) digits from 0 to 9. Every number (value) represents with 0,1,2,3,4,5,6, 7,8 and 9 in this number system. The base of decimal number system is 10, because it has only 10 digits.

A Hexadecimal number system has sixteen (16) alphanumeric values from 0 to 9 and A to F. Every number (value) represents with 0,1,2,3,4,5,6, 7,8,9,A,B,C,D,E and F in this number system. The base of the hexadecimal number system is 16, because it has 16 alphanumeric values.

Here A is 10, B is 11, C is 12, D is 13, E is 14 and F is 15 .

Data Representation of Characters

There are different methods to represent characters . Some of them are discussed below:

The code called ASCII (pronounced ‘􀀏’.S-key”), which stands for American Standard Code for Information Interchange, uses 7 bits to represent each character in computer memory. The ASCII representation has been adopted as a standard by the U.S. government and is widely accepted.

A unique integer number is assigned to each character. This number called ASCII code of that character is converted into binary for storing in memory. For example, the ASCII code of A is 65, its binary equivalent in 7-bit is 1000001.

Since there are exactly 128 unique combinations of 7 bits, this 7-bit code can represent only128 characters. Another version is ASCII-8, also called extended ASCII, which uses 8 bits for each character, can represent 256 different characters.

For example, the letter A is represented by 01000001, B by 01000010 and so on. ASCII code is enough to represent all of the standard keyboard characters.

It stands for Extended Binary Coded Decimal Interchange Code. This is similar to ASCII and is an 8-bit code used in computers manufactured by International Business Machines (IBM). It is capable of encoding 256 characters.

If ASCII-coded data is to be used in a computer that uses EBCDIC representation, it is necessary to transform ASCII code to EBCDIC code. Similarly, if EBCDIC coded data is to be used in an ASCII computer, EBCDIC code has to be transformed to ASCII.

ISCII stands for Indian Standard Code for Information Interchange or Indian Script Code for Information Interchange. It is an encoding scheme for representing various writing systems of India. ISCII uses 8-bits for data representation.

It was evolved by a standardization committee under the Department of Electronics during 1986-88 and adopted by the Bureau of Indian Standards (BIS). Nowadays ISCII has been replaced by Unicode.

Using 8-bit ASCII we can represent only 256 characters. This cannot represent all characters of written languages of the world and other symbols. Unicode is developed to resolve this problem. It aims to provide a standard character encoding scheme, which is universal and efficient.

It provides a unique number for every character, no matter what the language and platform be. Unicode originally used 16 bits which can represent up to 65,536 characters. It is maintained by a non-profit organization called the Unicode Consortium.

The Consortium first published version 1.0.0 in 1991 and continues to develop standards based on that original work. Nowadays Unicode uses more than 16 bits and hence it can represent more characters. Unicode can represent characters in almost all written languages of the world.

Data Representation of Audio, Image and Video

In most cases, we may have to represent and process data other than numbers and characters. This may include audio data, images, and videos. We can see that like numbers and characters, the audio, image, and video data also carry information.

We will see different file formats for storing sound, image, and video .

Multimedia data such as audio, image, and video are stored in different types of files. The variety of file formats is due to the fact that there are quite a few approaches to compressing the data and a number of different ways of packaging the data.

For example, an image is most popularly stored in Joint Picture Experts Group (JPEG ) file format. An image file consists of two parts – header information and image data. Information such as the name of the file, size, modified data, file format, etc. is stored in the header part.

The intensity value of all pixels is stored in the data part of the file. The data can be stored uncompressed or compressed to reduce the file size. Normally, the image data is stored in compressed form. Let us understand what compression is.

Take a simple example of a pure black image of size 400X400 pixels. We can repeat the information black, black, …, black in all 16,0000 (400X400) pixels. This is the uncompressed form, while in the compressed form black is stored only once and information to repeat it 1,60,000 times is also stored.

Numerous such techniques are used to achieve compression. Depending on the application, images are stored in various file formats such as bitmap file format (BMP), Tagged Image File Format (TIFF), Graphics Interchange Format (GIF), Portable (Public) Network Graphic (PNG).

What we said about the header file information and compression is also applicable for audio and video files. Digital audio data can be stored in different file formats like WAV, MP3, MIDI, AIFF, etc. An audio file describes a format, sometimes referred to as the ‘container format’, for storing digital audio data.

For example, WAV file format typically contains uncompressed sound and MP3 files typically contain compressed audio data. The synthesized music data is stored in MIDI(Musical Instrument Digital Interface) files.

Similarly, video is also stored in different files such as AVI (Audio Video Interleave) – a file format designed to store both audio and video data in a standard package that allows synchronous audio with video playback, MP3, JPEG-2, WMV, etc.

FAQs About Data Representation in Computer

What is number system with example.

Let us discuss some of the number systems. Computer architecture supports the following number of systems: 1. Binary Number System 2. Octal Number System 3. Decimal Number System 4. Hexadecimal Number System

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Computer Science: Reflections on the Field, Reflections from the Field (2004)

Chapter: 5 data, representation, and information, 5 data, representation, and information.

T he preceding two chapters address the creation of models that capture phenomena of interest and the abstractions both for data and for computation that reduce these models to forms that can be executed by computer. We turn now to the ways computer scientists deal with information, especially in its static form as data that can be manipulated by programs.

Gray begins by narrating a long line of research on databases—storehouses of related, structured, and durable data. We see here that the objects of research are not data per se but rather designs of “schemas” that allow deliberate inquiry and manipulation. Gray couples this review with introspection about the ways in which database researchers approach these problems.

Databases support storage and retrieval of information by defining—in advance—a complex structure for the data that supports the intended operations. In contrast, Lesk reviews research on retrieving information from documents that are formatted to meet the needs of applications rather than predefined schematized formats.

Interpretation of information is at the heart of what historians do, and Ayers explains how information technology is transforming their paradigms. He proposes that history is essentially model building—constructing explanations based on available information—and suggests that the methods of computer science are influencing this core aspect of historical analysis.

DATABASE SYSTEMS: A TEXTBOOK CASE OF RESEARCH PAYING OFF

Jim Gray, Microsoft Research

A small research investment helped produce U.S. market dominance in the $14 billion database industry. Government and industry funding of a few research projects created the ideas for several generations of products and trained the people who built those products. Continuing research is now creating the ideas and training the people for the next generation of products.

Industry Profile

The database industry generated about $14 billion in revenue in 2002 and is growing at 20 percent per year, even though the overall technology sector is almost static. Among software sectors, the database industry is second only to operating system software. Database industry leaders are all U.S.-based corporations: IBM, Microsoft, and Oracle are the three largest. There are several specialty vendors: Tandem sells over $1 billion/ year of fault-tolerant transaction processing systems, Teradata sells about $1 billion/year of data-mining systems, and companies like Information Resources Associates, Verity, Fulcrum, and others sell specialized data and text-mining software.

In addition to these well-established companies, there is a vibrant group of small companies specializing in application-specific databases—for text retrieval, spatial and geographical data, scientific data, image data, and so on. An emerging group of companies offer XML-oriented databases. Desktop databases are another important market focused on extreme ease of use, small size, and disconnected (offline) operation.

Historical Perspective

Companies began automating their back-office bookkeeping in the 1960s. The COBOL programming language and its record-oriented file model were the workhorses of this effort. Typically, a batch of transactions was applied to the old-tape-master, producing a new-tape-master and printout for the next business day. During that era, there was considerable experimentation with systems to manage an online database that could capture transactions as they happened. At first these systems were ad hoc, but late in that decade network and hierarchical database products emerged. A COBOL subcommittee defined a network data model stan-

dard (DBTG) that formed the basis for most systems during the 1970s. Indeed, in 1980 DBTG-based Cullinet was the leading software company.

However, there were some problems with DBTG. DBTG uses a low-level, record-at-a-time procedural language to access information. The programmer has to navigate through the database, following pointers from record to record. If the database is redesigned, as often happens over a decade, then all the old programs have to be rewritten.

The relational data model, enunciated by IBM researcher Ted Codd in a 1970 Communications of the Association for Computing Machinery article, 1 was a major advance over DBTG. The relational model unified data and metadata so that there was only one form of data representation. It defined a non-procedural data access language based on algebra or logic. It was easier for end users to visualize and understand than the pointers-and-records-based DBTG model.

The research community (both industry and university) embraced the relational data model and extended it during the 1970s. Most significantly, researchers showed that a non-procedural language could be compiled to give performance comparable to the best record-oriented database systems. This research produced a generation of systems and people that formed the basis for products from IBM, Ingres, Oracle, Informix, Sybase, and others. The SQL relational database language was standardized by ANSI/ISO between 1982 and 1986. By 1990, virtually all database systems provided an SQL interface (including network, hierarchical, and object-oriented systems).

Meanwhile the database research agenda moved on to geographically distributed databases and to parallel data access. Theoretical work on distributed databases led to prototypes that in turn led to products. Today, all the major database systems offer the ability to distribute and replicate data among nodes of a computer network. Intense research on data replication during the late 1980s and early 1990s gave rise to a second generation of replication products that are now the mainstays of mobile computing.

Research of the 1980s showed how to execute each of the relational data operators in parallel—giving hundred-fold and thousand-fold speedups. The results of this research began to appear in the products of several major database companies. With the proliferation of data mining in the 1990s, huge databases emerged. Interactive access to these databases requires that the system use multiple processors and multiple disks to read all the data in parallel. In addition, these problems require near-

linear time search algorithms. University and industrial research of the previous decade had solved these problems and forms the basis of the current VLDB (very large database) data-mining systems.

Rollup and drilldown data reporting systems had been a mainstay of decision-support systems ever since the 1960s. In the middle 1990s, the research community really focused on data-mining algorithms. They invented very efficient data cube and materialized view algorithms that form the basis for the current generation of business intelligence products.

The most recent round of government-sponsored research creating a new industry comes from the National Science Foundation’s Digital Libraries program, which spawned Google. It was founded by a group of “database” graduate students who took a fresh look at how information should be organized and presented in the Internet era.

Current Research Directions

There continues to be active and valuable research on representing and indexing data, adding inference to data search, compiling queries more efficiently, executing queries in parallel, integrating data from heterogeneous data sources, analyzing performance, and extending the transaction model to handle long transactions and workflow (transactions that involve human as well as computer steps). The availability of huge volumes of data on the Internet has prompted the study of data integration, mediation, and federation in which a portal system presents a unification of several data sources by pulling data on demand from different parts of the Internet.

In addition, there is great interest in unifying object-oriented concepts with the relational model. New data types (image, document, and drawing) are best viewed as the methods that implement them rather than by the bytes that represent them. By adding procedures to the database system, one gets active databases, data inference, and data encapsulation. This object-oriented approach is an area of active research and ferment both in academe and industry. It seems that in 2003, the research prototypes are mostly done and this is an area that is rapidly moving into products.

The Internet is full of semi-structured data—data that has a bit of schema and metadata, but is mostly a loose collection of facts. XML has emerged as the standard representation of semi-structured data, but there is no consensus on how such data should be stored, indexed, or searched. There have been intense research efforts to answer these questions. Prototypes have been built at universities and industrial research labs, and now products are in development.

The database research community now has a major focus on stream data processing. Traditionally, databases have been stored locally and are

updated by transactions. Sensor networks, financial markets, telephone calls, credit card transactions, and other data sources present streams of data rather than a static database. The stream data processing researchers are exploring languages and algorithms for querying such streams and providing approximate answers.

Now that nearly all information is online, data security and data privacy are extremely serious and important problems. A small, but growing, part of the database community is looking at ways to protect people’s privacy by limiting the ways data is used. This work also has implications for protecting intellectual property (e.g., digital rights management, watermarking) and protecting data integrity by digitally signing documents and then replicating them so that the documents cannot be altered or destroyed.

Case Histories

The U.S. government funded many database research projects from 1972 to the present. Projects at the University of California at Los Angeles gave rise to Teradata and produced many excellent students. Projects at Computer Corp. of America (SDD-1, Daplex, Multibase, and HiPAC) pioneered distributed database technology and object-oriented database technology. Projects at Stanford University fostered deductive database technology, data integration technology, query optimization technology, and the popular Yahoo! and Google Internet sites. Work at Carnegie Mellon University gave rise to general transaction models and ultimately to the Transarc Corporation. There have been many other successes from AT&T, the University of Texas at Austin, Brown and Harvard Universities, the University of Maryland, the University of Michigan, Massachusetts Institute of Technology, Princeton University, and the University of Toronto among others. It is not possible to enumerate all the contributions here, but we highlight three representative research projects that had a major impact on the industry.

Project INGRES

Project Ingres started at the University of California at Berkeley in 1972. Inspired by Codd’s paper on relational databases, several faculty members (Stonebraker, Rowe, Wong, and others) started a project to design and build a relational system. Incidental to this work, they invented a query language (QUEL), relational optimization techniques, a language binding technique, and interesting storage strategies. They also pioneered work on distributed databases.

The Ingres academic system formed the basis for the Ingres product now owned by Computer Associates. Students trained on Ingres went on

to start or staff all the major database companies (AT&T, Britton Lee, HP, Informix, IBM, Oracle, Tandem, Sybase). The Ingres project went on to investigate distributed databases, database inference, active databases, and extensible databases. It was rechristened Postgres, which is now the basis of the digital library and scientific database efforts within the University of California system. Recently, Postgres spun off to become the basis for a new object-relational system from the start-up Illustra Information Technologies.

Codd’s ideas were inspired by seeing the problems IBM and its customers were having with IBM’s IMS product and the DBTG network data model. His relational model was at first very controversial; people thought that the model was too simplistic and that it could never give good performance. IBM Research management took a gamble and chartered a small (10-person) systems effort to prototype a relational system based on Codd’s ideas. That system produced a prototype that eventually grew into the DB2 product series. Along the way, the IBM team pioneered ideas in query optimization, data independence (views), transactions (logging and locking), and security (the grant-revoke model). In addition, the SQL query language from System R was the basis for the ANSI/ISO standard.

The System R group went on to investigate distributed databases (project R*) and object-oriented extensible databases (project Starburst). These research projects have pioneered new ideas and algorithms. The results appear in IBM’s database products and those of other vendors.

Not all research ideas work out. During the 1970s there was great enthusiasm for database machines—special-purpose computers that would be much faster than general-purpose operating systems running conventional database systems. These research projects were often based on exotic hardware like bubble memories, head-per-track disks, or associative RAM. The problem was that general-purpose systems were improving at 50 percent per year, so it was difficult for exotic systems to compete with them. By 1980, most researchers realized the futility of special-purpose approaches and the database-machine community switched to research on using arrays of general-purpose processors and disks to process data in parallel.

The University of Wisconsin hosted the major proponents of this idea in the United States. Funded by the government and industry, those researchers prototyped and built a parallel database machine called

Gamma. That system produced ideas and a generation of students who went on to staff all the database vendors. Today the parallel systems from IBM, Tandem, Oracle, Informix, Sybase, and Microsoft all have a direct lineage from the Wisconsin research on parallel database systems. The use of parallel database systems for data mining is the fastest-growing component of the database server industry.

The Gamma project evolved into the Exodus project at Wisconsin (focusing on an extensible object-oriented database). Exodus has now evolved to the Paradise system, which combines object-oriented and parallel database techniques to represent, store, and quickly process huge Earth-observing satellite databases.

And Then There Is Science

In addition to creating a huge industry, database theory, science, and engineering constitute a key part of computer science today. Representing knowledge within a computer is one of the central challenges of computer science ( Box 5.1 ). Database research has focused primarily on this fundamental issue. Many universities have faculty investigating these problems and offer classes that teach the concepts developed by this research program.

COMPUTER SCIENCE IS TO INFORMATION AS CHEMISTRY IS TO MATTER

Michael Lesk, Rutgers University

In other countries computer science is often called “informatics” or some similar name. Much computer science research derives from the need to access, process, store, or otherwise exploit some resource of useful information. Just as chemistry is driven to large extent by the need to understand substances, computing is driven by a need to handle data and information. As an example of the way chemistry has developed, see Oliver Sacks’s book Uncle Tungsten: Memories of a Chemical Boyhood (Vintage Books, 2002). He describes his explorations through the different metals, learning the properties of each, and understanding their applications. Similarly, in the history of computer science, our information needs and our information capabilities have driven parts of the research agenda. Information retrieval systems take some kind of information, such as text documents or pictures, and try to retrieve topics or concepts based on words or shapes. Deducing the concept from the bytes can be difficult, and the way we approach the problem depends on what kind of bytes we have and how many of them we have.

Our experimental method is to see if we can build a system that will provide some useful access to information or service. If it works, those algorithms and that kind of data become a new field: look at areas like geographic information systems. If not, people may abandon the area until we see a new motivation to exploit that kind of data. For example, face-recognition algorithms have received a new impetus from security needs, speeding up progress in the last few years. An effective strategy to move computer science forward is to provide some new kind of information and see if we can make it useful.

Chemistry, of course, involves a dichotomy between substances and reactions. Just as we can (and frequently do) think of computer science in terms of algorithms, we can talk about chemistry in terms of reactions. However, chemistry has historically focused on substances: the encyclopedias and indexes in chemistry tend to be organized and focused on compounds, with reaction names and schemes getting less space on the shelf. Chemistry is becoming more balanced as we understand reactions better; computer science has always been more heavily oriented toward algorithms, but we cannot ignore the driving force of new kinds of data.

The history of information retrieval, for example, has been driven by the kinds of information we could store and use. In the 1960s, for example, storage was extremely expensive. Research projects were limited to text

materials. Even then, storage costs meant that a research project could just barely manage to have a single ASCII document available for processing. For example, Gerard Salton’s SMART system, one of the leading text retrieval systems for many years (see Salton’s book, The SMART Automatic Retrieval System , Prentice-Hall, 1971), did most of its processing on collections of a few hundred abstracts. The only collections of “full documents” were a collection of 80 extended abstracts, each a page or two long, and a collection of under a thousand stories from Time Magazine , each less than a page in length. The biggest collection was 1400 abstracts in aeronautical engineering. With this data, Salton was able to experiment on the effectiveness of retrieval methods using suffixing, thesauri, and simple phrase finding. Salton also laid down the standard methodology for evaluating retrieval systems, based on Cyril Cleverdon’s measures of “recall” (percentage of the relevant material that is retrieved in response to a query) and “precision” (the percentage of the material retrieved that is relevant). A system with perfect recall finds all relevant material, making no errors of omission and leaving out nothing the user wanted. In contrast, a system with perfect precision finds only relevant material, making no errors of commission and not bothering the user with stuff of no interest. The SMART system produced these measures for many retrieval experiments and its methodology was widely used, making text retrieval one of the earliest areas of computer science with agreed-on evaluation methods. Salton was not able to do anything with image retrieval at the time; there were no such data available for him.

Another idea shaped by the amount of information available was “relevance feedback,” the idea of identifying useful documents from a first retrieval pass in order to improve the results of a later retrieval. With so few documents, high precision seemed like an unnecessary goal. It was simply not possible to retrieve more material than somebody could look at. Thus, the research focused on high recall (also stimulated by the insistence by some users that they had to have every single relevant document). Relevance feedback helped recall. By contrast, the use of phrase searching to improve precision was tried but never got much attention simply because it did not have the scope to produce much improvement in the running systems.

The basic problem is that we wish to search for concepts, and what we have in natural language are words and phrases. When our documents are few and short, the main problem is not to miss any, and the research at the time stressed algorithms that found related words via associations or improved recall with techniques like relevance feedback.

Then, of course, several other advances—computer typesetting and word processing to generate material and cheap disks to hold it—led to much larger text collections. Figure 5.1 shows the decline in the price of

FIGURE 5.1 Decline in the price of disk space, 1950 to 2004.

disk space since the first disks in the mid-1950s, generally following the cost-performance trends of Moore’s law.

Cheaper storage led to larger and larger text collections online. Now there are many terabytes of data on the Web. These vastly larger volumes mean that precision has now become more important, since a common problem is to wade through vastly too many documents. Not surprisingly, in the mid-1980s efforts started on separating the multiple meanings of words like “bank” or “pine” and became the research area of “sense disambiguation.” 2 With sense disambiguation, it is possible to imagine searching for only one meaning of an ambiguous word, thus avoiding many erroneous retrievals.

Large-scale research on text processing took off with the availability of the TREC (Text Retrieval Evaluation Conference) data. Thanks to the National Institute of Standards and Technology, several hundred megabytes of text were provided (in each of several years) for research use. This stimulated more work on query analysis, text handling, searching

algorithms, and related areas; see the series titled TREC Conference Proceedings, edited by Donna Harmon of NIST.

Document clustering appeared as an important way to shorten long search results. Clustering enables a system to report not, say, 5000 documents but rather 10 groups of 500 documents each, and the user can then explore the group or groups that seem relevant. Salton anticipated the future possibility of such algorithms, as did others. 3 Until we got large collections, though, clustering did not find application in the document retrieval world. Now one routinely sees search engines using these techniques, and faster clustering algorithms have been developed.

Thus the algorithms explored switched from recall aids to precision aids as the quantity of available data increased. Manual thesauri, for example, have dropped out of favor for retrieval, partly because of their cost but also because their goal is to increase recall, which is not today’s problem. In terms of finding the concepts hinted at by words and phrases, our goals now are to sharpen rather than broaden these concepts: thus disambiguation and phrase matching, and not as much work on thesauri and term associations.

Again, multilingual searching started to matter, because multilingual collections became available. Multilingual research shows a more precise example of particular information resources driving research. The Canadian government made its Parliamentary proceedings (called Hansard ) available in both French and English, with paragraph-by-paragraph translation. This data stimulated a number of projects looking at how to handle bilingual material, including work on automatic alignment of the parallel texts, automatic linking of similar words in the two languages, and so on. 4

A similar effect was seen with the Brown corpus of tagged English text, where the part of speech of each word (e.g., whether a word is a noun or a verb) was identified. This produced a few years of work on algorithms that learned how to assign parts of speech to words in running text based on statistical techniques, such as the work by Garside. 5

One might see an analogy to various new fields of chemistry. The recognition that pesticides like DDT were environmental pollutants led to a new interest in biodegradability, and the Freon propellants used in aerosol cans stimulated research in reactions in the upper atmosphere. New substances stimulated a need to study reactions that previously had not been a top priority for chemistry and chemical engineering.

As storage became cheaper, image storage was now as practical as text storage had been a decade earlier. Starting in the 1980s we saw the IBM QBIC project demonstrating that something could be done to retrieve images directly, without having to index them by text words first. 6 Projects like this were stimulated by the availability of “clip art” such as the COREL image disks. Several different projects were driven by the easy access to images in this way, with technology moving on from color and texture to more accurate shape processing. At Berkeley, for example, the “Blobworld” project made major improvements in shape detection and recognition, as described in Carson et al. 7 These projects demonstrated that retrieval could be done with images as well as with words, and that properties of images could be found that were usable as concepts for searching.

Another new kind of data that became feasible to process was sound, in particular human speech. Here it was the Defense Advanced Research Projects Agency (DARPA) that took the lead, providing the SWITCH-BOARD corpus of spoken English. Again, the availability of a substantial file of tagged information helped stimulate many research projects that used this corpus and developed much of the technology that eventually went into the commercial speech recognition products we now have. As with the TREC contests, the competitions run by DARPA based on its spoken language data pushed the industry and the researchers to new advances. National needs created a new technology; one is reminded of the development of synthetic rubber during World War II or the advances in catalysis needed to make explosives during World War I.

Yet another kind of new data was geo-coded data, introducing a new set of conceptual ideas related to place. Geographical data started showing up in machine-readable form during the 1980s, especially with the release of the Dual Independent Map Encoding (DIME) files after the 1980

census and the Topologically Integrated Geographic Encoding and Referencing (TIGER) files from the 1990 census. The availability, free of charge, of a complete U.S. street map stimulated much research on systems to display maps, to give driving directions, and the like. 8 When aerial photographs also became available, there was the triumph of Microsoft’s “Terraserver,” which made it possible to look at a wide swath of the world from the sky along with correlated street and topographic maps. 9

More recently, in the 1990s, we have started to look at video search and retrieval. After all, if a CD-ROM contains about 300,000 times as many bytes per pound as a deck of punched cards, and a digitized video has about 500,000 times as many bytes per second as the ASCII script it comes from, we should be about where we were in the 1960s with video today. And indeed there are a few projects, most notably the Informedia project at Carnegie Mellon University, that experiment with video signals; they do not yet have ways of searching enormous collections, but they are developing algorithms that exploit whatever they can find in the video: scene breaks, closed-captioning, and so on.

Again, there is the problem of deducing concepts from a new kind of information. We started with the problem of words in one language needing to be combined when synonymous, picked apart when ambiguous, and moved on to detecting synonyms across multiple languages and then to concepts depicted in pictures and sounds. Now we see research such as that by Jezekiel Ben-Arie associating words like “run” or “hop” with video images of people doing those actions. In the same way we get again new chemistry when molecules like “buckyballs” are created and stimulate new theoretical and reaction studies.

Defining concepts for search can be extremely difficult. For example, despite our abilities to parse and define every item in a computer language, we have made no progress on retrieval of software; people looking for search or sort routines depend on metadata or comments. Some areas seem more flexible than others: text and naturalistic photograph processing software tends to be very general, while software to handle CAD diagrams and maps tends to be more specific. Algorithms are sometimes portable; both speech processing and image processing need Fourier transforms, but the literature is less connected than one might like (partly

because of the difference between one-dimensional and two-dimensional transforms).

There are many other examples of interesting computer science research stimulated by the availability of particular kinds of information. Work on string matching today is often driven by the need to align sequences in either protein or DNA data banks. Work on image analysis is heavily influenced by the need to deal with medical radiographs. And there are many other interesting projects specifically linked to an individual data source. Among examples:

The British Library scanning of the original manuscript of Beowulf in collaboration with the University of Kentucky, working on image enhancement until the result of the scanning is better than reading the original;

The Perseus project, demonstrating the educational applications possible because of the earlier Thesaurus Linguae Graecae project, which digitized all the classical Greek authors;

The work in astronomical analysis stimulated by the Sloan Digital Sky Survey;

The creation of the field of “forensic paleontology” at the University of Texas as a result of doing MRI scans of fossil bones;

And, of course, the enormous amount of work on search engines stimulated by the Web.

When one of these fields takes off, and we find wide usage of some online resource, it benefits society. Every university library gained readers as their catalogs went online and became accessible to students in their dorm rooms. Third World researchers can now access large amounts of technical content their libraries could rarely acquire in the past.

In computer science, and in chemistry, there is a tension between the algorithm/reaction and the data/substance. For example, should one look up an answer or compute it? Once upon a time logarithms were looked up in tables; today we also compute them on demand. Melting points and other physical properties of chemical substances are looked up in tables; perhaps with enough quantum mechanical calculation we could predict them, but it’s impractical for most materials. Predicting tomorrow’s weather might seem a difficult choice. One approach is to measure the current conditions, take some equations that model the atmosphere, and calculate forward a day. Another is to measure the current conditions, look in a big database for the previous day most similar to today, and then take the day after that one as the best prediction for tomorrow. However, so far the meteorologists feel that calculation is better. Another complicated example is chess: given the time pressure of chess tournaments

against speed and storage available in computers, chess programs do the opening and the endgame by looking in tables of old data and calculate for the middle game.

To conclude, a recipe for stimulating advances in computer science is to make some data available and let people experiment with it. With the incredibly cheap disks and scanners available today, this should be easier than ever. Unfortunately, what we gain with technology we are losing to law and economics. Many large databases are protected by copyright; few motion pictures, for example, are old enough to have gone out of copyright. Content owners generally refuse to grant permission for wide use of their material, whether out of greed or fear: they may have figured out how to get rich off their files of information or they may be afraid that somebody else might have. Similarly it is hard to get permission to digitize in-copyright books, no matter how long they have been out of print. Jim Gray once said to me, “May all your problems be technical.” In the 1960s I was paying people to key in aeronautical abstracts. It never occurred to us that we should be asking permission of the journals involved (I think what we did would qualify as fair use, but we didn’t even think about it). Today I could scan such things much more easily, but I would not be able to get permission. Am I better off or worse off?

There are now some 22 million chemical substances in the Chemical Abstracts Service Registry and 7 million reactions. New substances continue to intrigue chemists and cause research on new reactions, with of course enormous interest in biochemistry both for medicine and agriculture. Similarly, we keep adding data to the Web, and new kinds of information (photographs of dolphins, biological flora, and countless other things) can push computer scientists to new algorithms. In both cases, synthesis of specific instances into concepts is a crucial problem. As we see more and more kinds of data, we learn more about how to extract meaning from it, and how to present it, and we develop a need for new algorithms to implement this knowledge. As the data gets bigger, we learn more about optimization. As it gets more complex, we learn more about representation. And as it gets more useful, we learn more about visualization and interfaces, and we provide better service to society.

HISTORY AND THE FUNDAMENTALS OF COMPUTER SCIENCE

Edward L. Ayers, University of Virginia

We might begin with a thought experiment: What is history? Many people, I’ve discovered, think of it as books and the things in books. That’s certainly the explicit form in which we usually confront history. Others, thinking less literally, might think of history as stories about the past; that would open us to oral history, family lore, movies, novels, and the other forms in which we get most of our history.

All these images are wrong, of course, in the same way that images of atoms as little solar systems are wrong, or pictures of evolution as profiles of ever taller and more upright apes and people are wrong. They are all models, radically simplified, that allow us to think about such things in the exceedingly small amounts of time that we allot to these topics.

The same is true for history, which is easiest to envision as technological progress, say, or westward expansion, of the emergence of freedom—or of increasing alienation, exploitation of the environment, or the growth of intrusive government.

Those of us who think about specific aspects of society or nature for a living, of course, are never satisfied with the stories that suit the purposes of everyone else so well.

We are troubled by all the things that don’t fit, all the anomalies, variance, and loose ends. We demand more complex measurement, description, and fewer smoothing metaphors and lowest common denominators.

Thus, to scientists, atoms appear as clouds of probability; evolution appears as a branching, labyrinthine bush in which some branches die out and others diversify. It can certainly be argued that past human experience is as complex as anything in nature and likely much more so, if by complexity we mean numbers of components, variability of possibilities, and unpredictability of outcomes.

Yet our means of conveying that complexity remain distinctly analog: the story, the metaphor, the generalization. Stories can be wonderfully complex, of course, but they are complex in specific ways: of implication, suggestion, evocation. That’s what people love and what they remember.

But maybe there is a different way of thinking about the past: as information. In fact, information is all we have. Studying the past is like studying scientific processes for which you have the data but cannot run the experiment again, in which there is no control, and in which you can never see the actual process you are describing and analyzing. All we have is information in various forms: words in great abundance, billions of numbers, millions of images, some sounds and buildings, artifacts.

The historian’s goal, it seems to me, should be to account for as much of the complexity embedded in that information as we can. That, it appears, is what scientists do, and it has served them well.

And how has science accounted for ever-increasing amounts of complexity in the information they use? Through ever more sophisticated instruments. The connection between computer science and history could be analogous to that between telescopes and stars, microscopes and cells. We could be on the cusp of a new understanding of the patterns of complexity in human behavior of the past.

The problem may be that there is too much complexity in that past, or too much static, or too much silence. In the sciences, we’ve learned how to filter, infer, use indirect evidence, and fill in the gaps, but we have a much more literal approach to the human past.

We have turned to computer science for tasks of more elaborate description, classification, representation. The digital archive my colleagues and I have built, the Valley of the Shadow Project, permits the manipulation of millions of discrete pieces of evidence about two communities in the era of the American Civil War. It uses sorting mechanisms, hypertextual display, animation, and the like to allow people to handle the evidence of this part of the past for themselves. This isn’t cutting-edge computer science, of course, but it’s darned hard and deeply disconcerting to some, for it seems to abdicate responsibility, to undermine authority, to subvert narrative, to challenge story.

Now, we’re trying to take this work to the next stage, to analysis. We have composed a journal article that employs an array of technologies, especially geographic information systems and statistical analysis in the creation of the evidence. The article presents its argument, evidence, and historiographical context as a complex textual, tabular, and graphical representation. XML offers a powerful means to structure text and XSL an even more powerful means to transform it and manipulate its presentation. The text is divided into sections called “statements,” each supported with “explanation.” Each explanation, in turn, is supported by evidence and connected to relevant historiography.

Linkages, forward and backward, between evidence and narrative are central. The historiography can be automatically sorted by author, date, or title; the evidence can be arranged by date, topic, or type. Both evidence and historiographical entries are linked to the places in the analysis where they are invoked. The article is meant to be used online, but it can be printed in a fixed format with all the limitations and advantages of print.

So, what are the implications of thinking of the past in the hardheaded sense of admitting that all we really have of the past is information? One implication might be great humility, since all we have for most

of the past are the fossils of former human experience, words frozen in ink and images frozen in line and color. Another implication might be hubris: if we suddenly have powerful new instruments, might we be on the threshold of a revolution in our understanding of the past? We’ve been there before.

A connection between history and social science was tried before, during the first days of accessible computers. Historians taught themselves statistical methods and even programming languages so that they could adopt the techniques, models, and insights of sociology and political science. In the 1950s and 1960s the creators of the new political history called on historians to emulate the precision, explicitness, replicability, and inclusivity of the quantitative social sciences. For two decades that quantitative history flourished, promising to revolutionize the field. And to a considerable extent it did: it changed our ideas of social mobility, political identification, family formation, patterns of crime, economic growth, and the consequences of ethnic identity. It explicitly linked the past to the present and held out a history of obvious and immediate use.

But that quantitative social science history collapsed suddenly, the victim of its own inflated claims, limited method and machinery, and changing academic fashion. By the mid-1980s, history, along with many of the humanities and social sciences, had taken the linguistic turn. Rather than software manuals and codebooks, graduate students carried books of French philosophy and German literary interpretation. The social science of choice shifted from sociology to anthropology; texts replaced tables. A new generation defined itself in opposition to social scientific methods just as energetically as an earlier generation had seen in those methods the best means of writing a truly democratic history. The first computer revolution largely failed.

The first effort at that history fell into decline in part because historians could not abide the distance between their most deeply held beliefs and what the statistical machinery permitted, the abstraction it imposed. History has traditionally been built around contingency and particularity, but the most powerful tools of statistics are built on sampling and extrapolation, on generalization and tendency. Older forms of social history talked about vague and sometimes dubious classifications in part because that was what the older technology of tabulation permitted us to see. It has become increasingly clear across the social sciences that such flat ways of describing social life are inadequate; satisfying explanations must be dynamic, interactive, reflexive, and subtle, refusing to reify structures of social life or culture. The new technology permits a new cross-fertilization.

Ironically, social science history faded just as computers became widely available, just as new kinds of social science history became feasible. No longer is there any need for white-coated attendants at huge mainframes

and expensive proprietary software. Rather than reducing people to rows and columns, searchable databases now permit researchers to maintain the identities of individuals in those databases and to represent entire populations rather than samples. Moreover, the record can now include things social science history could only imagine before the Web: completely indexed newspapers, with the original readable on the screen; completely searchable letters and diaries by the thousands; and interactive maps with all property holders identified and linked to other records. Visualization of patterns in the data, moreover, far outstrips the possibilities of numerical calculation alone. Manipulable histograms, maps, and time lines promise a social history that is simultaneously sophisticated and accessible. We have what earlier generations of social science historians dreamed of: a fast and widely accessible network linked to cheap and powerful computers running common software with well-established standards for the handling of numbers, texts, and images. New possibilities of collaboration and cumulative research beckon. Perhaps the time is right to reclaim a worthy vision of a disciplined and explicit social scientific history that we abandoned too soon.

What does this have to do with computer science? Everything, it seems to me. If you want hard problems, historians have them. And what’s the hardest problem of all right now? The capture of the very information that is history. Can computer science imagine ways to capture historical information more efficiently? Can it offer ways to work with the spotty, broken, dirty, contradictory, nonstandardized information we work with?

The second hard problem is the integration of this disparate evidence in time and space, offering new precision, clarity, and verifiability, as well as opening new questions and new ways of answering them.

If we can think of these ways, then we face virtually limitless possibilities. Is there a more fundamental challenge or opportunity for computer science than helping us to figure out human society over human time?

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Computer Science: Reflections on the Field, Reflections from the Field provides a concise characterization of key ideas that lie at the core of computer science (CS) research. The book offers a description of CS research recognizing the richness and diversity of the field. It brings together two dozen essays on diverse aspects of CS research, their motivation and results. By describing in accessible form computer science’s intellectual character, and by conveying a sense of its vibrancy through a set of examples, the book aims to prepare readers for what the future might hold and help to inspire CS researchers in its creation.

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• Math Article

Graphical Representation

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ideas, information and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

• Line Graphs – Line graph or the linear graph is used to display the continuous data and it is useful for predicting future events over time.
• Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.
• Histograms – The graph that uses bars to represent the frequency of numerical data that are organised into intervals. Since all the intervals are equal and continuous, all the bars have the same width.
• Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.
• Frequency Table – The table shows the number of pieces of data that falls within the given interval.
• Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered with 100% and the categories occupied is represented with that specific percentage like 15%, 56%, etc.
• Stem and Leaf Plot – In the stem and leaf plot, the data are organised from least value to the greatest value. The digits of the least place values from the leaves and the next place value digit forms the stems.
• Box and Whisker Plot – The plot diagram summarises the data by dividing into four parts. Box and whisker show the range (spread) and the middle ( median) of the data.

General Rules for Graphical Representation of Data

There are certain rules to effectively present the information in the graphical representation. They are:

• Suitable Title: Make sure that the appropriate title is given to the graph which indicates the subject of the presentation.
• Measurement Unit: Mention the measurement unit in the graph.
• Proper Scale: To represent the data in an accurate manner, choose a proper scale.
• Index: Index the appropriate colours, shades, lines, design in the graphs for better understanding.
• Data Sources: Include the source of information wherever it is necessary at the bottom of the graph.
• Keep it Simple: Construct a graph in an easy way that everyone can understand.
• Neat: Choose the correct size, fonts, colours etc in such a way that the graph should be a visual aid for the presentation of information.

Graphical Representation in Maths

In Mathematics, a graph is defined as a chart with statistical data, which are represented in the form of curves or lines drawn across the coordinate point plotted on its surface. It helps to study the relationship between two variables where it helps to measure the change in the variable amount with respect to another variable within a given interval of time. It helps to study the series distribution and frequency distribution for a given problem.  There are two types of graphs to visually depict the information. They are:

• Time Series Graphs – Example: Line Graph
• Frequency Distribution Graphs – Example: Frequency Polygon Graph

Principles of Graphical Representation

Algebraic principles are applied to all types of graphical representation of data. In graphs, it is represented using two lines called coordinate axes. The horizontal axis is denoted as the x-axis and the vertical axis is denoted as the y-axis. The point at which two lines intersect is called an origin ‘O’. Consider x-axis, the distance from the origin to the right side will take a positive value and the distance from the origin to the left side will take a negative value. Similarly, for the y-axis, the points above the origin will take a positive value, and the points below the origin will a negative value.

Generally, the frequency distribution is represented in four methods, namely

• Smoothed frequency graph
• Pie diagram
• Cumulative or ogive frequency graph
• Frequency Polygon

Merits of Using Graphs

Some of the merits of using graphs are as follows:

• The graph is easily understood by everyone without any prior knowledge.
• It saves time
• It allows us to relate and compare the data for different time periods
• It is used in statistics to determine the mean, median and mode for different data, as well as in the interpolation and the extrapolation of data.

Example for Frequency polygonGraph

Here are the steps to follow to find the frequency distribution of a frequency polygon and it is represented in a graphical way.

• Obtain the frequency distribution and find the midpoints of each class interval.
• Represent the midpoints along x-axis and frequencies along the y-axis.
• Plot the points corresponding to the frequency at each midpoint.
• Join these points, using lines in order.
• To complete the polygon, join the point at each end immediately to the lower or higher class marks on the x-axis.

Draw the frequency polygon for the following data

Mark the class interval along x-axis and frequencies along the y-axis.

Let assume that class interval 0-10 with frequency zero and 90-100 with frequency zero.

Now calculate the midpoint of the class interval.

Using the midpoint and the frequency value from the above table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

To obtain the frequency polygon ABCDEFGHIJ, draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ, and connect all the points.

Frequently Asked Questions

What are the different types of graphical representation.

Some of the various types of graphical representation include:

• Line Graphs
• Frequency Table
• Circle Graph, etc.

Read More:  Types of Graphs

What are the Advantages of Graphical Method?

Some of the advantages of graphical representation are:

• It makes data more easily understandable.
• It saves time.
• It makes the comparison of data more efficient.

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Very useful for understand the basic concepts in simple and easy way. Its very useful to all students whether they are school students or college sudents

Thanks very much for the information

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Table of contents.

• Introduction to Functional Computer
• Fundamentals of Architectural Design

Data Representation

• Instruction Set Architecture : Instructions and Formats
• Instruction Set Architecture : Design Models
• Instruction Set Architecture : Addressing Modes
• Performance Measurements and Issues
• Computer Architecture Assessment 1
• Fixed Point Arithmetic : Addition and Subtraction
• Fixed Point Arithmetic : Multiplication
• Fixed Point Arithmetic : Division
• Floating Point Arithmetic
• Arithmetic Logic Unit Design
• CPU's Data Path
• CPU's Control Unit
• Control Unit Design
• Concepts of Pipelining
• Computer Architecture Assessment 2
• Pipeline Hazards
• Memory Characteristics and Organization
• Cache Memory
• Virtual Memory
• I/O Communication and I/O Controller
• Input/Output Data Transfer
• Direct Memory Access controller and I/O Processor
• CPU Interrupts and Interrupt Handling
• Computer Architecture Assessment 3

Course Computer Architecture

Digital computers store and process information in binary form as digital logic has only two values "1" and "0" or in other words "True or False" or also said as "ON or OFF". This system is called radix 2. We human generally deal with radix 10 i.e. decimal. As a matter of convenience there are many other representations like Octal (Radix 8), Hexadecimal (Radix 16), Binary coded decimal (BCD), Decimal etc.

Every computer's CPU has a width measured in terms of bits such as 8 bit CPU, 16 bit CPU, 32 bit CPU etc. Similarly, each memory location can store a fixed number of bits and is called memory width. Given the size of the CPU and Memory, it is for the programmer to handle his data representation. Most of the readers may be knowing that 4 bits form a Nibble, 8 bits form a byte. The word length is defined by the Instruction Set Architecture of the CPU. The word length may be equal to the width of the CPU.

The memory simply stores information as a binary pattern of 1's and 0's. It is to be interpreted as what the content of a memory location means. If the CPU is in the Fetch cycle, it interprets the fetched memory content to be instruction and decodes based on Instruction format. In the Execute cycle, the information from memory is considered as data. As a common man using a computer, we think computers handle English or other alphabets, special characters or numbers. A programmer considers memory content to be data types of the programming language he uses. Now recall figure 1.2 and 1.3 of chapter 1 to reinforce your thought that conversion happens from computer user interface to internal representation and storage.

• Data Representation in Computers

Information handled by a computer is classified as instruction and data. A broad overview of the internal representation of the information is illustrated in figure 3.1. No matter whether it is data in a numeric or non-numeric form or integer, everything is internally represented in Binary. It is up to the programmer to handle the interpretation of the binary pattern and this interpretation is called Data Representation . These data representation schemes are all standardized by international organizations.

Choice of Data representation to be used in a computer is decided by

• The number types to be represented (integer, real, signed, unsigned, etc.)
• Range of values likely to be represented (maximum and minimum to be represented)
• The Precision of the numbers i.e. maximum accuracy of representation (floating point single precision, double precision etc)
• If non-numeric i.e. character, character representation standard to be chosen. ASCII, EBCDIC, UTF are examples of character representation standards.
• The hardware support in terms of word width, instruction.

Before we go into the details, let us take an example of interpretation. Say a byte in Memory has value "0011 0001". Although there exists a possibility of so many interpretations as in figure 3.2, the program has only one interpretation as decided by the programmer and declared in the program.

• Fixed point Number Representation

Fixed point numbers are also known as whole numbers or Integers. The number of bits used in representing the integer also implies the maximum number that can be represented in the system hardware. However for the efficiency of storage and operations, one may choose to represent the integer with one Byte, two Bytes, Four bytes or more. This space allocation is translated from the definition used by the programmer while defining a variable as integer short or long and the Instruction Set Architecture.

In addition to the bit length definition for integers, we also have a choice to represent them as below:

• Unsigned Integer : A positive number including zero can be represented in this format. All the allotted bits are utilised in defining the number. So if one is using 8 bits to represent the unsigned integer, the range of values that can be represented is 28 i.e. "0" to "255". If 16 bits are used for representing then the range is 216 i.e. "0 to 65535".
• Signed Integer : In this format negative numbers, zero, and positive numbers can be represented. A sign bit indicates the magnitude direction as positive or negative. There are three possible representations for signed integer and these are Sign Magnitude format, 1's Compliment format and 2's Complement format .

Signed Integer – Sign Magnitude format: Most Significant Bit (MSB) is reserved for indicating the direction of the magnitude (value). A "0" on MSB means a positive number and a "1" on MSB means a negative number. If n bits are used for representation, n-1 bits indicate the absolute value of the number. Examples for n=8:

Examples for n=8:

0010 1111 = + 47 Decimal (Positive number)

1010 1111 = - 47 Decimal (Negative Number)

0111 1110 = +126 (Positive number)

1111 1110 = -126 (Negative Number)

0000 0000 = + 0 (Postive Number)

1000 0000 = - 0 (Negative Number)

Although this method is easy to understand, Sign Magnitude representation has several shortcomings like

• Zero can be represented in two ways causing redundancy and confusion.
• The total range for magnitude representation is limited to 2n-1, although n bits were accounted.
• The separate sign bit makes the addition and subtraction more complicated. Also, comparing two numbers is not straightforward.

Signed Integer – 1’s Complement format: In this format too, MSB is reserved as the sign bit. But the difference is in representing the Magnitude part of the value for negative numbers (magnitude) is inversed and hence called 1’s Complement form. The positive numbers are represented as it is in binary. Let us see some examples to better our understanding.

1101 0000 = - 47 Decimal (Negative Number)

1000 0001 = -126 (Negative Number)

1111 1111 = - 0 (Negative Number)

• Converting a given binary number to its 2's complement form

Step 1 . -x = x' + 1 where x' is the one's complement of x.

Step 2 Extend the data width of the number, fill up with sign extension i.e. MSB bit is used to fill the bits.

Example: -47 decimal over 8bit representation

As you can see zero is not getting represented with redundancy. There is only one way of representing zero. The other problem of the complexity of the arithmetic operation is also eliminated in 2’s complement representation. Subtraction is done as Addition.

More exercises on number conversion are left to the self-interest of readers.

• Floating Point Number system

The maximum number at best represented as a whole number is 2 n . In the Scientific world, we do come across numbers like Mass of an Electron is 9.10939 x 10-31 Kg. Velocity of light is 2.99792458 x 108 m/s. Imagine to write the number in a piece of paper without exponent and converting into binary for computer representation. Sure you are tired!!. It makes no sense to write a number in non- readable form or non- processible form. Hence we write such large or small numbers using exponent and mantissa. This is said to be Floating Point representation or real number representation. he real number system could have infinite values between 0 and 1.

Representation in computer

Unlike the two's complement representation for integer numbers, Floating Point number uses Sign and Magnitude representation for both mantissa and exponent . In the number 9.10939 x 1031, in decimal form, +31 is Exponent, 9.10939 is known as Fraction . Mantissa, Significand and fraction are synonymously used terms. In the computer, the representation is binary and the binary point is not fixed. For example, a number, say, 23.345 can be written as 2.3345 x 101 or 0.23345 x 102 or 2334.5 x 10-2. The representation 2.3345 x 101 is said to be in normalised form.

Floating-point numbers usually use multiple words in memory as we need to allot a sign bit, few bits for exponent and many bits for mantissa. There are standards for such allocation which we will see sooner.

• IEEE 754 Floating Point Representation

We have two standards known as Single Precision and Double Precision from IEEE. These standards enable portability among different computers. Figure 3.3 picturizes Single precision while figure 3.4 picturizes double precision. Single Precision uses 32bit format while double precision is 64 bits word length. As the name suggests double precision can represent fractions with larger accuracy. In both the cases, MSB is sign bit for the mantissa part, followed by Exponent and Mantissa. The exponent part has its sign bit.

It is to be noted that in Single Precision, we can represent an exponent in the range -127 to +127. It is possible as a result of arithmetic operations the resulting exponent may not fit in. This situation is called overflow in the case of positive exponent and underflow in the case of negative exponent. The Double Precision format has 11 bits for exponent meaning a number as large as -1023 to 1023 can be represented. The programmer has to make a choice between Single Precision and Double Precision declaration using his knowledge about the data being handled.

The Floating Point operations on the regular CPU is very very slow. Generally, a special purpose CPU known as Co-processor is used. This Co-processor works in tandem with the main CPU. The programmer should be using the float declaration only if his data is in real number form. Float declaration is not to be used generously.

• Decimal Numbers Representation

Decimal numbers (radix 10) are represented and processed in the system with the support of additional hardware. We deal with numbers in decimal format in everyday life. Some machines implement decimal arithmetic too, like floating-point arithmetic hardware. In such a case, the CPU uses decimal numbers in BCD (binary coded decimal) form and does BCD arithmetic operation. BCD operates on radix 10. This hardware operates without conversion to pure binary. It uses a nibble to represent a number in packed BCD form. BCD operations require not only special hardware but also decimal instruction set.

• Exceptions and Error Detection

All of us know that when we do arithmetic operations, we get answers which have more digits than the operands (Ex: 8 x 2= 16). This happens in computer arithmetic operations too. When the result size exceeds the allotted size of the variable or the register, it becomes an error and exception. The exception conditions associated with numbers and number operations are Overflow, Underflow, Truncation, Rounding and Multiple Precision . These are detected by the associated hardware in arithmetic Unit. These exceptions apply to both Fixed Point and Floating Point operations. Each of these exceptional conditions has a flag bit assigned in the Processor Status Word (PSW). We may discuss more in detail in the later chapters.

• Character Representation

Another data type is non-numeric and is largely character sets. We use a human-understandable character set to communicate with computer i.e. for both input and output. Standard character sets like EBCDIC and ASCII are chosen to represent alphabets, numbers and special characters. Nowadays Unicode standard is also in use for non-English language like Chinese, Hindi, Spanish, etc. These codes are accessible and available on the internet. Interested readers may access and learn more.

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What are the different ways of Data Representation?

• What are the Different Kinds of Data Scientists?
• Different types of Coding Schemes to represent data
• Graphical Representation of Data
• What are the types of statistics?
• Textual Presentation of Data: Meaning, Suitability, and Drawbacks
• Diagrammatic and Graphic Presentation of Data
• Different Types of Data in Data Mining
• Tabular Presentation of Data: Meaning, Objectives, Features and Merits
• What is a Dataset: Types, Features, and Examples
• Data Manipulation: Definition, Examples, and Uses
• Collection and Presentation of Data
• What is Data Organization?
• Different forms of data representation in today's world
• Difference Between Presentation and Representation
• What are the Basic Data Types in PHP ?
• Processing of Raw Data to Tidy Data in R
• Graph and its representations
• Difference between Information and Data
• Data Preprocessing and Its Types

The process of collecting the data and analyzing that data in large quantity is known as statistics. It is a branch of mathematics trading with the collection, analysis, interpretation, and presentation of numeral facts and figures.

It is a numerical statement that helps us to collect and analyze the data in large quantity the statistics are based on two of its concepts:

• Statistical Data 
• Statistical Science

Statistics must be expressed numerically and should be collected systematically.

Data Representation

The word data refers to constituting people, things, events, ideas. It can be a title, an integer, or anycast.  After collecting data the investigator has to condense them in tabular form to study their salient features. Such an arrangement is known as the presentation of data.

It refers to the process of condensing the collected data in a tabular form or graphically. This arrangement of data is known as Data Representation.

The row can be placed in different orders like it can be presented in ascending orders, descending order, or can be presented in alphabetical order. 

Example: Let the marks obtained by 10 students of class V in a class test, out of 50 according to their roll numbers, be: 39, 44, 49, 40, 22, 10, 45, 38, 15, 50 The data in the given form is known as raw data. The above given data can be placed in the serial order as shown below: Roll No. Marks 1 39 2 44 3 49 4 40 5 22 6 10 7 45 8 38 9 14 10 50 Now, if you want to analyse the standard of achievement of the students. If you arrange them in ascending or descending order, it will give you a better picture. Ascending order: 10, 15, 22, 38, 39, 40, 44. 45, 49, 50 Descending order: 50, 49, 45, 44, 40, 39, 38, 22, 15, 10 When the row is placed in ascending or descending order is known as arrayed data.

Types of Graphical Data Representation

Bar chart helps us to represent the collected data visually. The collected data can be visualized horizontally or vertically in a bar chart like amounts and frequency. It can be grouped or single. It helps us in comparing different items. By looking at all the bars, it is easy to say which types in a group of data influence the other.

Now let us understand bar chart by taking this example  Let the marks obtained by 5 students of class V in a class test, out of 10 according to their names, be: 7,8,4,9,6 The data in the given form is known as raw data. The above given data can be placed in the bar chart as shown below: Name Marks Akshay 7 Maya 8 Dhanvi 4 Jaslen 9 Muskan 6

A histogram is the graphical representation of data. It is similar to the appearance of a bar graph but there is a lot of difference between histogram and bar graph because a bar graph helps to measure the frequency of categorical data. A categorical data means it is based on two or more categories like gender, months, etc. Whereas histogram is used for quantitative data.

For example:

The graph which uses lines and points to present the change in time is known as a line graph. Line graphs can be based on the number of animals left on earth, the increasing population of the world day by day, or the increasing or decreasing the number of bitcoins day by day, etc. The line graphs tell us about the changes occurring across the world over time. In a  line graph, we can tell about two or more types of changes occurring around the world.

For Example:

Pie chart is a type of graph that involves a structural graphic representation of numerical proportion. It can be replaced in most cases by other plots like a bar chart, box plot, dot plot, etc. As per the research, it is shown that it is difficult to compare the different sections of a given pie chart, or if it is to compare data across different pie charts.

Frequency Distribution Table

A frequency distribution table is a chart that helps us to summarise the value and the frequency of the chart. This frequency distribution table has two columns, The first column consist of the list of the various outcome in the data, While the second column list the frequency of each outcome of the data. By putting this kind of data into a table it helps us to make it easier to understand and analyze the data. 

For Example: To create a frequency distribution table, we would first need to list all the outcomes in the data. In this example, the results are 0 runs, 1 run, 2 runs, and 3 runs. We would list these numerals in numerical ranking in the foremost queue. Subsequently, we ought to calculate how many times per result happened. They scored 0 runs in the 1st, 4th, 7th, and 8th innings, 1 run in the 2nd, 5th, and the 9th innings, 2 runs in the 6th inning, and 3 runs in the 3rd inning. We set the frequency of each result in the double queue. You can notice that the table is a vastly more useful method to show this data.  Baseball Team Runs Per Inning Number of Runs Frequency           0       4           1        3            2        1            3        1

Sample Questions

Question 1: Considering the school fee submission of 10 students of class 10th is given below:

In order to draw the bar graph for the data above, we prepare the frequency table as given below. Fee submission No. of Students Paid   6 Not paid    4 Now we have to represent the data by using the bar graph. It can be drawn by following the steps given below: Step 1: firstly we have to draw the two axis of the graph X-axis and the Y-axis. The varieties of the data must be put on the X-axis (the horizontal line) and the frequencies of the data must be put on the Y-axis (the vertical line) of the graph. Step 2: After drawing both the axis now we have to give the numeric scale to the Y-axis (the vertical line) of the graph It should be started from zero and ends up with the highest value of the data. Step 3: After the decision of the range at the Y-axis now we have to give it a suitable difference of the numeric scale. Like it can be 0,1,2,3…….or 0,10,20,30 either we can give it a numeric scale like 0,20,40,60… Step 4: Now on the X-axis we have to label it appropriately. Step 5: Now we have to draw the bars according to the data but we have to keep in mind that all the bars should be of the same length and there should be the same distance between each graph

Question 2: Watch the subsequent pie chart that denotes the money spent by Megha at the funfair. The suggested colour indicates the quantity paid for each variety. The total value of the data is 15 and the amount paid on each variety is diagnosed as follows:

Chocolates – 3

Wafers – 3

Toys – 2

Rides – 7

To convert this into pie chart percentage, we apply the formula:  (Frequency/Total Frequency) × 100 Let us convert the above data into a percentage: Amount paid on rides: (7/15) × 100 = 47% Amount paid on toys: (2/15) × 100 = 13% Amount paid on wafers: (3/15) × 100 = 20% Amount paid on chocolates: (3/15) × 100 = 20 %

Question 3: The line graph given below shows how Devdas’s height changes as he grows.

Given below is a line graph showing the height changes in Devdas’s as he grows. Observe the graph and answer the questions below.

(i) What was the height of  Devdas’s at 8 years? Answer: 65 inches (ii) What was the height of  Devdas’s at 6 years? Answer:  50 inches (iii) What was the height of  Devdas’s at 2 years? Answer: 35 inches (iv) How much has  Devdas’s grown from 2 to 8 years? Answer: 30 inches (v) When was  Devdas’s 35 inches tall? Answer: 2 years.

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This is the first stop on your way to mastering the essentials of data curation for the humanities. The Guide offers concise, expert introductions to key topics, including annotated links to important standards, articles, projects, and other resources.

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Data curation is an emerging problem for the humanities as both data and analytical practices become increasingly digital. Research groups working with cultural content as well as libraries, museums, archives, and other institutions are all in need of new expertise. This Guide is a first step to understanding the essentials of data curation for the humanities. The expert-written introductions to key topics include links to important standards, documentation, articles, and projects in the field, annotated with enough context from expert editors and the research community to indicate to newcomers how these resources might help them with data curation challenges.

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Digital twins: The art of the possible in product development and beyond

Industrial companies around the world rely on digital tools to turn ideas into physical products for their customers. These tools have become increasingly more powerful, flexible, and sophisticated since the 1960s and 1970s, when computers first began replacing drawing boards in design offices. Today, product life-cycle management (PLM) has become engineers’ first language: PLM systems help companies to capture, codify, process, and communicate product knowledge across their organizations.

About the authors

This article is a collaborative effort by Mickael Brossard , Sebastien Chaigne, Jacomo Corbo, Bernhard Mühlreiter , and Jan Paul Stein, representing views from McKinsey’s Operations Practice.

Yet as engineering tools have become more capable, the demands placed upon them have also increased. Product functions are increasingly delivered through a combination of hardware and software. Sensors and communications capabilities allow products to offer more features and to respond more effectively to changing operating conditions and user requirements. Advanced, adaptable user interfaces have simplified the operation of complex and sophisticated machines.

Evolving business models are also blurring the boundaries between design and use. Customers expect the performance and functionality of products to improve during their life cycle, enabled by over-the-air software updates or the ability to unlock new features as needed. Many products operate as part of an ecosystem of related products and services. Increasingly, customers are not buying products outright, but paying for the capabilities they provide on a per-use or subscription basis.

The birth of the digital twin

These changing requirements have triggered a transformation in digital product representation and the creation of a new tool: the digital twin. Digital twins combine and build upon existing digital engineering tools, incorporating additional data sources, adding advanced simulation and analytics capabilities, and establishing links to live data generated during the product’s manufacture and use. A conventional PLM system uses one digital model to represent each variant of a product. A digital twin, by contrast, may have one model for each individual product, which is continually updated using data collected during the product’s life cycle.

The digital-twin approach can be applied to products, manufacturing processes, or even entire value chains. In this article, we will focus on their application to products, specifically to product design.

Digital twins offer multiple potential benefits for product-based companies and users. They can aid design optimization, reduce costs and time to market, and accelerate the organization’s response to new customer needs. Digital twins can also be a critical enabler of new revenue streams, such as remote maintenance and support offerings and “as a service” business models.

Based on the experience of companies that have already adopted the approach, we estimate that digital-twin technologies can drive a revenue increase of up to 10 percent, accelerate time to market by as much as 50 percent, and improve product quality by up to 25 percent. Digital-twin technology  is becoming a significant industry. Current estimates indicate that the market for digital twins in Europe alone will be around €7 billion by 2025, with an annual growth rate of 30 to 45 percent. 1 Infinium; MarketsandMarkets; MarkNTel Advisors; Meticulous Market Research; Mordor Intelligence; SBIS; Technavio, last accessed April 2020.

Digital twins in practice

Companies in many different industries are already capturing real value by applying digital twins to product development , manufacturing, and through-life support (exhibit).

An automotive OEM, for example, has used the digital-twin approach to create a concept configurator for early phase development . The start of the development process is especially challenging for complex products because the various stakeholder groups, such as sales, engineering, and finance, may have different or even contradictory product requirements. The OEM now balances these trade-offs using a digital concept configurator that allows for simultaneous evaluation of customer requirements, technical concepts, and product costs. When a technical concept within a system or subsystem of the product is changed, the implications for meeting customer requirements or product cost targets become immediately transparent.

Would you like to learn more about our work in Product Digital Twins ?

Using the configurator within cross-functional development teams has helped the OEM to reallocate 5 to 15 percent of a new vehicle’s material costs to the attributes that drive the most customer value. Applying the approach to select customer-facing components has allowed the company to optimize costs and customer value simultaneously, improving the contribution margin of those parts by 5 to 10 percent. As a further benefit, the configurator helped the team reduce the time taken to reach agreement on changes by 20 percent, thus accelerating time to market.

Digital twins are even being used to replicate systems in complex mission scenarios. Using this approach, one aerospace and defense player has cut the time required to develop advanced products by 30 to 40 percent. The digital twin also aids discussion with customers during the development process, helping the company validate and improve its designs.

In the consumer electronics sector, a company is using product digital twins to boost quality and supply chain resilience . It stores detailed information on the content of its products, including the exact source of individual components. In the event of quality issues during production or early failures in the field, the company can trace problems back to specific supplier facilities, then take appropriate action to prevent reoccurrence of the issue. An automotive supplier uses the same approach to trace quality deviations in its production through to the upstream supply chain, and in the process has reduced scrap by 20 percent.

Digital twins are increasingly being used to improve future product generations . An electric-vehicle (EV) manufacturer, for example, uses live data from more than 80 sensors to track energy consumption under different driving regimes and in varying weather conditions. Analysis of that data allows it to upgrade its vehicle control software, with some updates introduced into new vehicles and others delivered over the air to existing customers.

Developers of autonomous-driving systems , meanwhile, are increasingly developing their technology in virtual environments. The training and validation of algorithms in a simulated environment is safer and cheaper than real-world tests. Moreover, the ability to run numerous simulations in parallel has accelerated the testing process by more than 10,000 times. Incorporating sensor data from real-world vehicles into these tests helps companies improve the veracity of their simulations and identify blind spots in the virtual test database.

The mainstreaming of additive manufacturing

A company in the renewable-energy sector is using a digital twin to automate, accelerate, and improve the engineering of hydroelectric turbines . Using the machine learning system to evaluate the likely performance of the new designs allowed it to rate more than a million different designs in seconds rather than the hours required for conventional computational flow dynamics (CFD) analysis. The winning geometry delivers the maximum theoretical performance, significantly higher than what is achievable by conventional optimization methods. Moreover, by using machine learning, the overall end-to-end design cycle time was cut in half compared with the conventional approach.

Digital twins in three dimensions

Digital twins can take many different forms. Organizations that want to take advantage of digital-twin technologies must select an appropriate form that will enhance its technical and business objectives. The design of a digital twin can vary across three dimensions (exhibit).

The first dimension encompasses the value chain steps that the digital twin will cover. An engineering twin covers value chain steps similar to those covered by conventional PLM systems, ranging from product definition to detailed engineering. A production twin replicates a product throughout the manufacturing process, incorporating data such as the components, materials, and process parameters used, as well as the results of tests and quality checks. A service twin incorporates data collected from the product in use, such as operating modes, performance, diagnostic information, and maintenance history. The most sophisticated digital twins span multiple parts of the value chain, allowing in-service data to optimize manufacturing processes or future design iterations.

The second dimension is the scope of the digital twin. A product may consist of several major systems, multiple subsystems, and hundreds or thousands of hardware and software components. Some digital twins cover only one or several components, for example, those that simulate the flow of liquids through a pipe. Others cover a full product, for example, those that simulate a car’s crash characteristics. Given the limitations of computing power, generally, the narrower the scope of a digital twin, the more precise its virtual replica will be. In contrast, full-product digital twins often need to abstract or simplify certain product behaviors to remain manageable.

The final dimension of a digital twin is its degree of sophistication . The simplest digital twins consist of various sources of data relating to a product, often from sources that have few or no links with one another. The second level of sophistication uses traditional simulation tools to perform analyses of design performance and integrate the various sources through a PLM system or similar platform.

At the third level of sophistication, a digital twin will use predictive or prescriptive analytics, as well as machine learning technology to run automated simulation refinements and yield new insights. This allows design and manufacturing teams to make informed decisions based upon direct results and performances.

At the last level of sophistication, digital twins use predictions of component failure rates or performance variations to react to changing environments and manipulate the real-world counterpart in a closed-loop setup. This approach might be used in a condition monitoring system, for example, where sensor data and simulations are combined to make inferences and predictions about the state and behavior of a specific product, and might allow a machine to compensate for wear or variations in operating conditions by adjusting parameters in real time.

Companies in other sectors are also starting to use digital twins to derive deeper insights into customer behaviors and preferences . For example, white-goods manufacturers can use data from in-service products to identify the most and least used features. That can inform future product development decisions, such as deleting rarely used features or revising the user interface to make the features more accessible.

The adoption of digital twins is currently gaining momentum across industries, as companies aim to reap the benefits of various types of digital twins. Given the many different shapes and forms of digital twins (see sidebar, “Digital twins in three dimensions”), and the different starting points of each organization, a clear strategy is needed to help prioritize where to focus digital-twin development and what steps to take to capture the most value.

How to start and succeed on your digital-twin journey

Embarking on a digital-twin journey can look daunting at first sight, especially since the breadth and depth of use cases can span the entire corporate landscape, including product portfolio choices, business model design, R&D, manufacturing, and through-life support.

This versatility can also be a strength, however, as it allows companies to start small and expand the scope, sophistication, and value-chain coverage of their digital-twin projects over time. The experience of companies that have applied digital twins in their own product operations leads to a few simple rules that can greatly increase your odds of success.

Define your aspirations

Be aware of digital-twin best practices. Do your homework and seek out perspectives on best practices and future trends in digital-twin technology. Assess and prioritize the elements of your vision. Evaluate the potential of digital-twin-related opportunities and prioritize them into an implementation road map.

Be clear about the business case. Quantify the value offered by different digital-twin opportunities and determine the minimum level of model sophistication required to generate that value. Successful projects focus on short development times and rapid ROI.

Test the waters by prototyping select use cases. Run a series of hackathons (possibly supported by digital-twin specialists) to assess your capabilities’ baseline, develop solution prototypes, refine, and adjust the initial concepts. This step calibrates the approach and prevents you from losing time and resources by attempting an impossible plan. It is part of a broader value assurance move aimed at bringing the entire project to a successful conclusion.

Know your strengths

Perform a maturity assessment. Understand your current digital product development capabilities along six main dimensions: development methodologies, PLM governance, data strategy, business processes, system complexity, and collaboration. Understanding the areas where you are most advanced and where you are lagging behind will help prioritize areas of investment for a balanced implementation of a digital twin and its use cases.

Access to appropriate talent and capabilities can make or break a digital-twin initiative. Many organizations need to develop additional expertise in areas such as advanced simulation and modeling or data analytics for user experience design.

Plan a step-by-step, agile implementation

Invest several months in developing a minimum viable product (MVP). Incubate a cross-functional, agile team dedicated to bringing priority use cases to life and building digital capabilities in the process. The MVP is now the must-do approach to maximize value gains from the start rather than waiting until the program is finalized before experiencing the first benefits.

Perform an MVP retrospective to pivot or persevere. Derive lessons from the first MVP phase to confirm your digital-twin aspirations or pivot them based on the findings (for example, the validity of use cases, complexity of implementation, and maturity of the organization). This is the second value assurance move that enables you to further calibrate the implementation plan and revise the scope to avoid generating sunk costs.

Scale up the digital-twin initiative and accelerate ROI. Optimize and standardize implementation based on insights from the MVP phase. Define an (internal or external) recruiting and capability-building strategy. Build an operating model to enable rapid scaling of successful approaches. The most advanced organizations typically consider digital-twin technologies a core strategic capability.

By following these simple best practices, you will be able to reap the benefits of digital twins in a scalable, progressive way. Are you ready?

Mickael Brossard is a partner in McKinsey’s Paris office, where Sebastien Chaigne is an associate partner; Jacomo Corbo is a partner in the London office; Bernhard Mühlreiter is a partner in the Vienna office; and Jan Paul Stein is an associate partner in the Munich office.

The authors wish to thank Roberto Argolini, Elia Berteletti, Kimberly Borden, Akshay Desai, Hannes Erntell, Alessandro Faure Ragani, Anna Herlt, Mark Huntington, Mithun Kamat, Michele Manzo, and Alessandro Mattozzi for their contributions to this article.

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Early iterations of the AI applications we interact with most today were built on traditional machine learning models. These models rely on learning algorithms that are developed and maintained by data scientists. In other words, traditional machine learning models need human intervention to process new information and perform any new task that falls outside their initial training.

For example, Apple made Siri a feature of its iOS in 2011. This early version of Siri was trained to understand a set of highly specific statements and requests. Human intervention was required to expand Siri’s knowledge base and functionality.

However, AI capabilities have been evolving steadily since the breakthrough development of  artificial neural networks  in 2012, which allow machines to engage in reinforcement learning and simulate how the human brain processes information.

Unlike basic machine learning models, deep learning models allow AI applications to learn how to perform new tasks that need human intelligence, engage in new behaviors and make decisions without human intervention. As a result, deep learning has enabled task automation, content generation, predictive maintenance and other capabilities across  industries .

Due to deep learning and other advancements, the field of AI remains in a constant and fast-paced state of flux. Our collective understanding of realized AI and theoretical AI continues to shift, meaning AI categories and AI terminology may differ (and overlap) from one source to the next. However, the types of AI can be largely understood by examining two encompassing categories: AI capabilities and AI functionalities.

1. Artificial Narrow AI

Artificial Narrow Intelligence, also known as Weak AI (what we refer to as Narrow AI), is the only type of AI that exists today. Any other form of AI is theoretical. It can be trained to perform a single or narrow task, often far faster and better than a human mind can.

However, it can’t perform outside of its defined task. Instead, it targets a single subset of cognitive abilities and advances in that spectrum. Siri, Amazon’s Alexa and IBM Watson are examples of Narrow AI. Even OpenAI’s ChatGPT is considered a form of Narrow AI because it’s limited to the single task of text-based chat.

2. General AI

Artificial General Intelligence (AGI), also known as  Strong AI , is today nothing more than a theoretical concept. AGI can use previous learnings and skills to accomplish new tasks in a different context without the need for human beings to train the underlying models. This ability allows AGI to learn and perform any intellectual task that a human being can.

3. Super AI

Super AI is commonly referred to as artificial superintelligence and, like AGI, is strictly theoretical. If ever realized, Super AI would think, reason, learn, make judgements and possess cognitive abilities that surpass those of human beings.

The applications possessing Super AI capabilities will have evolved beyond the point of understanding human sentiments and experiences to feel emotions, have needs and possess beliefs and desires of their own.

Underneath Narrow AI, one of the three types based on capabilities, there are two functional AI categories:

1. Reactive Machine AI

Reactive machines are AI systems with no memory and are designed to perform a very specific task. Since they can’t recollect previous outcomes or decisions, they only work with presently available data. Reactive AI stems from statistical math and can analyze vast amounts of data to produce a seemingly intelligent output.

Examples of Reactive Machine AI  

• IBM Deep Blue: IBM’s chess-playing supercomputer AI beat chess grandmaster Garry Kasparov in the late 1990s by analyzing the pieces on the board and predicting the probable outcomes of each move.
• The Netflix Recommendation Engine: Netflix’s viewing recommendations are powered by models that process data sets collected from viewing history to provide customers with content they’re most likely to enjoy.

2. Limited Memory AI

Unlike Reactive Machine AI, this form of AI can recall past events and outcomes and monitor specific objects or situations over time. Limited Memory AI can use past- and present-moment data to decide on a course of action most likely to help achieve a desired outcome.

However, while Limited Memory AI can use past data for a specific amount of time, it can’t retain that data in a library of past experiences to use over a long-term period. As it’s trained on more data over time, Limited Memory AI can improve in performance.

Examples of Limited Memory AI  

• Generative AI: Generative AI tools such as ChatGPT, Bard and DeepAI rely on limited memory AI capabilities to predict the next word, phrase or visual element within the content it’s generating.
• Virtual assistants and chatbots: Siri, Alexa, Google Assistant, Cortana and IBM Watson Assistant combine natural language processing (NLP) and Limited Memory AI to understand questions and requests, take appropriate actions and compose responses.
• Self-driving cars: Autonomous vehicles use Limited Memory AI to understand the world around them in real-time and make informed decisions on when to apply speed, brake, make a turn, etc.

3. Theory of Mind AI

Theory of Mind AI is a functional class of AI that falls underneath the General AI. Though an unrealized form of AI today, AI with Theory of Mind functionality would understand the thoughts and emotions of other entities. This understanding can affect how the AI interacts with those around them. In theory, this would allow the AI to simulate human-like relationships.

Because Theory of Mind AI could infer human motives and reasoning, it would personalize its interactions with individuals based on their unique emotional needs and intentions. Theory of Mind AI would also be able to understand and contextualize artwork and essays, which today’s generative AI tools are unable to do.

Emotion AI is a theory of mind AI currently in development. AI researchers hope it will have the ability to analyze voices, images and other kinds of data to recognize, simulate, monitor and respond appropriately to humans on an emotional level. To date, Emotion AI is unable to understand and respond to human feelings.  

4. Self-Aware AI

Self-Aware AI is a kind of functional AI class for applications that would possess super AI capabilities. Like theory of mind AI, Self-Aware AI is strictly theoretical. If ever achieved, it would have the ability to understand its own internal conditions and traits along with human emotions and thoughts. It would also have its own set of emotions, needs and beliefs.

Emotion AI is a Theory of Mind AI currently in development. Researchers hope it will have the ability to analyze voices, images and other kinds of data to recognize, simulate, monitor and respond appropriately to humans on an emotional level. To date, Emotion AI is unable to understand and respond to human feelings.

Computer vision

Narrow AI applications with  computer vision  can be trained to interpret and analyze the visual world. This allows intelligent machines to identify and classify objects within images and video footage.

Applications of computer vision include:

• Image recognition and classification
• Object detection
• Object tracking
• Facial recognition
• Content-based image retrieval

Computer vision is critical for use cases that involve AI machines interacting and traversing the physical world around them. Examples include self-driving cars and machines navigating warehouses and other environments.

Robots in industrial settings can use Narrow AI to perform routine, repetitive tasks that involve materials handling, assembly and quality inspections. In healthcare, robots equipped with Narrow AI can assist surgeons in monitoring vitals and detecting potential issues during procedures.

Agricultural machines can engage in autonomous pruning, moving, thinning, seeding and spraying. And smart home devices such as the iRobot Roomba can navigate a home’s interior using computer vision and use data stored in memory to understand its progress.

Expert systems

Expert systems equipped with Narrow AI capabilities can be trained on a corpus to emulate the human decision-making process and apply expertise to solve complex problems. These systems can evaluate vast amounts of data to uncover trends and patterns to make decisions. They can also help businesses predict future events and understand why past events occurred.

IBM has pioneered AI from the very beginning, contributing breakthrough after breakthrough to the field. IBM most recently released a big upgrade to its cloud-based, generative AI platform known as watsonx.  IBM watsonx.ai  brings together new generative AI capabilities, powered by foundation models and traditional machine learning into a powerful studio spanning the entire AI lifecycle. With watsonx.ai, data scientists can build, train and deploy machine learning models in a single collaborative studio environment.

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