data representation computer science worksheet

Data representations

Curriculum > KS4 > Unit

This unit allows learners to gain the understanding and skills required for the data representation sections of the GCSE computer science exam. First, learners look at binary and hexadecimal numbering systems, how they work, and how to convert between bases. Then, learners explore different coding systems and find out how text, images, and sound are represented in computers. All lessons include worksheets to allow learners to explore each topic through practical application.

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Summative assessment, summative answer.

• Lesson 1 What is representation? Log in to download
• Lesson 2 Number bases Log in to download
• Lesson 3 Binary addition Log in to download
• Lesson 4 Binary subtraction Log in to download
• Lesson 5 Binary shifts Log in to download
• Lesson 6 Signed binary integers Log in to download
• Lesson 7 Hexadecimal Log in to download
• Lesson 8 Representing text Log in to download
• Lesson 9 Unicode and file size calculation Log in to download
• Lesson 10 Representing bitmap images Log in to download
• Lesson 11 Bitmap file size calculation Log in to download
• Lesson 12 Representing sound Log in to download
• Lesson 13 Sound file size calculation Log in to download
• Lesson 14 Measurements of storage Log in to download
• Lesson 15 Lossy and lossless compression Log in to download
• Lesson 16 Run length encoding Log in to download
• Lesson 17 Huffman coding Log in to download
• Lesson 18 Summative assessment Log in to download

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Data Representation Worksheets

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Description

Five data representation worksheets / activities for students – ideal for a quick plenary, starter, revision task or quick quiz to keep the topic alive.

Great to use alongside our data representation recap videos, if needed.

Each worksheet requires students to complete an example of all six conversions, with space for their workings.  Answers included.

• Binary to denary
• Binary to hex
• Hex to binary
• Hex to denary
• Denary to hex
• Denary to binary

This resource is available now for an immediate digital download in PDF format.

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Data Representation

Class 11 - computer science with python sumita arora, checkpoint 2.1.

What are the bases of decimal, octal, binary and hexadecimal systems ?

The bases are:

• Decimal — Base 10
• Octal — Base 8
• Binary — Base 2
• Hexadecimal — Base 16

What is the common property of decimal, octal, binary and hexadecimal number systems ?

Decimal, octal, binary and hexadecimal number systems are all positional-value system .

Complete the sequence of following binary numbers : 100, 101, 110, ............... , ............... , ............... .

100, 101, 110, 111 , 1000 , 1001 .

Complete the sequence of following octal numbers : 525, 526, 527, ............... , ............... , ............... .

525, 526, 527, 530 , 531 , 532 .

Complete the sequence of following hexadecimal numbers : 17, 18, 19, ............... , ............... , ............... .

17, 18, 19, 1A , 1B , 1C .

Convert the following binary numbers to decimal and hexadecimal:

(c) 101011111

(e) 10010101

(f) 11011100

Converting to decimal:

Equivalent decimal number = 8 + 2 = 10

Therefore, (1010) 2 = (10) 10

Converting to hexadecimal:

Grouping in bits of 4:

1010 undefined \underlinesegment{1010} 1010 ​

Therefore, (1010) 2 = (A) 16

Equivalent decimal number = 32 + 16 + 8 + 2 = 58

Therefore, (111010) 2 = (58) 10

0011 undefined 1010 undefined \underlinesegment{0011} \quad \underlinesegment{1010} 0011 ​ 1010 ​

Therefore, (111010) 2 = (3A) 16

Equivalent decimal number = 256 + 64 + 16 + 8 + 4 + 2 + 1 = 351

Therefore, (101011111) 2 = (351) 10

0001 undefined 0101 undefined 1111 undefined \underlinesegment{0001} \quad \underlinesegment{0101} \quad \underlinesegment{1111} 0001 ​ 0101 ​ 1111 ​

Therefore, (101011111) 2 = (15F) 16

Equivalent decimal number = 8 + 4 = 12

Therefore, (1100) 2 = (12) 10

1100 undefined \underlinesegment{1100} 1100 ​

Therefore, (1100) 2 = (C) 16

Equivalent decimal number = 1 + 4 + 16 + 128 = 149

Therefore, (10010101) 2 = (149) 10

1001 undefined 0101 undefined \underlinesegment{1001} \quad \underlinesegment{0101} 1001 ​ 0101 ​

Therefore, (101011111) 2 = (95) 16

Equivalent decimal number = 4 + 8 + 16 + 64 + 128 = 220

Therefore, (11011100) 2 = (220) 10

1101 undefined 1100 undefined \underlinesegment{1101} \quad \underlinesegment{1100} 1101 ​ 1100 ​

Therefore, (11011100) 2 = (DC) 16

Convert the following decimal numbers to binary and octal :

Converting to binary:

Therefore, (23) 10 = (10111) 2

Converting to octal:

Therefore, (23) 10 = (27) 8

Therefore, (100) 10 = (1100100) 2

Therefore, (100) 10 = (144) 8

Therefore, (145) 10 = (10010001) 2

Therefore, (145) 10 = (221) 8

Therefore, (19) 10 = (10011) 2

Therefore, (19) 10 = (23) 8

Therefore, (121) 10 = (1111001) 2

Therefore, (121) 10 = (171) 8

Therefore, (161) 10 = (10100001) 2

Therefore, (161) 10 = (241) 8

Convert the following hexadecimal numbers to binary :

(A6) 16 = (10100110) 2

(A07) 16 = (101000000111) 2

(7AB4) 16 = (111101010110100) 2

(BE) 16 = (10111110) 2

(BC9) 16 = (101111001001) 2

(9BC8) 16 = (1001101111001000) 2

Convert the following binary numbers to hexadecimal and octal :

(a) 10011011101

(b) 1111011101011011

(c) 11010111010111

(d) 1010110110111

(e) 10110111011011

(f) 1111101110101111

0100 undefined 1101 undefined 1101 undefined \underlinesegment{0100} \quad \underlinesegment{1101} \quad \underlinesegment{1101} 0100 ​ 1101 ​ 1101 ​

Therefore, (10011011101) 2 = (4DD) 16

Converting to Octal:

Grouping in bits of 3:

010 undefined 011 undefined 011 undefined 101 undefined \underlinesegment{010} \quad \underlinesegment{011} \quad \underlinesegment{011} \quad \underlinesegment{101} 010 ​ 011 ​ 011 ​ 101 ​

Therefore, (10011011101) 2 = (2335) 8

1111 undefined 0111 undefined 0101 undefined 1011 undefined \underlinesegment{1111} \quad \underlinesegment{0111} \quad \underlinesegment{0101} \quad \underlinesegment{1011} 1111 ​ 0111 ​ 0101 ​ 1011 ​

Therefore, (1111011101011011) 2 = (F75B) 16

001 undefined 111 undefined 011 undefined 101 undefined 011 undefined 011 undefined \underlinesegment{001} \quad \underlinesegment{111} \quad \underlinesegment{011} \quad \underlinesegment{101} \quad \underlinesegment{011} \quad \underlinesegment{011} 001 ​ 111 ​ 011 ​ 101 ​ 011 ​ 011 ​

Therefore, (1111011101011011) 2 = (173533) 8

0011 undefined 0101 undefined 1101 undefined 0111 undefined \underlinesegment{0011} \quad \underlinesegment{0101} \quad \underlinesegment{1101} \quad \underlinesegment{0111} 0011 ​ 0101 ​ 1101 ​ 0111 ​

Therefore, (11010111010111) 2 = (35D7) 16

011 undefined 010 undefined 111 undefined 010 undefined 111 undefined \underlinesegment{011} \quad \underlinesegment{010} \quad \underlinesegment{111} \quad \underlinesegment{010} \quad \underlinesegment{111} 011 ​ 010 ​ 111 ​ 010 ​ 111 ​

Therefore, (11010111010111) 2 = (32727) 8

0001 undefined 0101 undefined 1011 undefined 0111 undefined \underlinesegment{0001} \quad \underlinesegment{0101} \quad \underlinesegment{1011} \quad \underlinesegment{0111} 0001 ​ 0101 ​ 1011 ​ 0111 ​

Therefore, (1010110110111) 2 = (15B7) 16

001 undefined 010 undefined 110 undefined 110 undefined 111 undefined \underlinesegment{001} \quad \underlinesegment{010} \quad \underlinesegment{110} \quad \underlinesegment{110} \quad \underlinesegment{111} 001 ​ 010 ​ 110 ​ 110 ​ 111 ​

Therefore, (1010110110111) 2 = (12667) 8

0010 undefined 1101 undefined 1101 undefined 1011 undefined \underlinesegment{0010} \quad \underlinesegment{1101} \quad \underlinesegment{1101} \quad \underlinesegment{1011} 0010 ​ 1101 ​ 1101 ​ 1011 ​

Therefore, (10110111011011) 2 = (2DDB) 16

010 undefined 110 undefined 111 undefined 011 undefined 011 undefined \underlinesegment{010} \quad \underlinesegment{110} \quad \underlinesegment{111} \quad \underlinesegment{011} \quad \underlinesegment{011} 010 ​ 110 ​ 111 ​ 011 ​ 011 ​

Therefore, (10110111011011) 2 = (26733) 8

1111 undefined 1011 undefined 1010 undefined 1111 undefined \underlinesegment{1111} \quad \underlinesegment{1011} \quad \underlinesegment{1010} \quad \underlinesegment{1111} 1111 ​ 1011 ​ 1010 ​ 1111 ​

Therefore, (1111101110101111) 2 = (FBAF) 16

001 undefined 111 undefined 101 undefined 110 undefined 101 undefined 111 undefined \underlinesegment{001} \quad \underlinesegment{111} \quad \underlinesegment{101} \quad \underlinesegment{110} \quad \underlinesegment{101} \quad \underlinesegment{111} 001 ​ 111 ​ 101 ​ 110 ​ 101 ​ 111 ​

Therefore, (1111101110101111) 2 = (175657) 8

Checkpoint 2.2

Multiple choice questions.

The value of radix in binary number system is ..........

The value of radix in octal number system is ..........

The value of radix in decimal number system is ..........

The value of radix in hexadecimal number system is ..........

Which of the following are not valid symbols in octal number system ?

Which of the following are not valid symbols in hexadecimal number system ?

Which of the following are not valid symbols in decimal number system ?

The hexadecimal digits are 1 to 0 and A to ..........

The binary equivalent of the decimal number 10 is ..........

Question 10

ASCII code is a 7 bit code for ..........

• other symbol
• all of these ✓

Question 11

How many bytes are there in 1011 1001 0110 1110 numbers?

Question 12

The binary equivalent of the octal Numbers 13.54 is.....

• 1101.1110 ✓
• None of these

Question 13

The octal equivalent of 111 010 is.....

Question 14

The input hexadecimal representation of 1110 is ..........

Question 15

Which of the following is not a binary number ?

Question 16

Convert the hexadecimal number 2C to decimal:

Question 17

UTF8 is a type of .......... encoding.

• extended ASCII

Question 18

UTF32 is a type of .......... encoding.

Question 19

Which of the following is not a valid UTF8 representation?

• 2 octet (16 bits)
• 3 octet (24 bits)
• 4 octet (32 bits)
• 8 octet (64 bits) ✓

Question 20

Which of the following is not a valid encoding scheme for characters ?

Fill in the Blanks

The Decimal number system is composed of 10 unique symbols.

The Binary number system is composed of 2 unique symbols.

The Octal number system is composed of 8 unique symbols.

The Hexadecimal number system is composed of 16 unique symbols.

The illegal digits of octal number system are 8 and 9 .

Hexadecimal number system recognizes symbols 0 to 9 and A to F .

Each octal number is replaced with 3 bits in octal to binary conversion.

Each Hexadecimal number is replaced with 4 bits in Hex to binary conversion.

ASCII is a 7 bit code while extended ASCII is a 8 bit code.

The Unicode encoding scheme can represent all symbols/characters of most languages.

The ISCII encoding scheme represents Indian Languages' characters on computers.

UTF8 can take upto 4 bytes to represent a symbol.

UTF32 takes exactly 4 bytes to represent a symbol.

Unicode value of a symbol is called code point .

True/False Questions

A computer can work with Decimal number system. False

A computer can work with Binary number system. True

The number of unique symbols in Hexadecimal number system is 15. False

Number systems can also represent characters. False

ISCII is an encoding scheme created for Indian language characters. True

Unicode is able to represent nearly all languages' characters. True

UTF8 is a fixed-length encoding scheme. False

UTF32 is a fixed-length encoding scheme. True

UTF8 is a variable-length encoding scheme and can represent characters in 1 through 4 bytes. True

UTF8 and UTF32 are the only encoding schemes supported by Unicode. False

Type A: Short Answer Questions

What are some number systems used by computers ?

The most commonly used number systems are decimal, binary, octal and hexadecimal number systems.

What is the use of Hexadecimal number system on computers ?

The Hexadecimal number system is used in computers to specify memory addresses (which are 16-bit or 32-bit long). For example, a memory address 1101011010101111 is a big binary address but with hex it is D6AF which is easier to remember. The Hexadecimal number system is also used to represent colour codes. For example, FFFFFF represents White, FF0000 represents Red, etc.

What does radix or base signify ?

The radix or base of a number system signifies how many unique symbols or digits are used in the number system to represent numbers. For example, the decimal number system has a radix or base of 10 meaning it uses 10 digits from 0 to 9 to represent numbers.

What is the use of encoding schemes ?

Encoding schemes help Computers represent and recognize letters, numbers and symbols. It provides a predetermined set of codes for each recognized letter, number and symbol. Most popular encoding schemes are ASCI, Unicode, ISCII, etc.

Discuss UTF-8 encoding scheme.

UTF-8 is a variable width encoding that can represent every character in Unicode character set. The code unit of UTF-8 is 8 bits called an octet. It uses 1 to maximum 6 octets to represent code points depending on their size i.e. sometimes it uses 8 bits to store the character, other times 16 or 24 or more bits. It is a type of multi-byte encoding.

How is UTF-8 encoding scheme different from UTF-32 encoding scheme ?

UTF-8 is a variable length encoding scheme that uses different number of bytes to represent different characters whereas UTF-32 is a fixed length encoding scheme that uses exactly 4 bytes to represent all Unicode code points.

What is the most significant bit and the least significant bit in a binary code ?

In a binary code, the leftmost bit is called the most significant bit or MSB. It carries the largest weight. The rightmost bit is called the least significant bit or LSB. It carries the smallest weight. For example:

1 M S B 0 1 1 0 1 1 0 L S B \begin{matrix} \underset{\bold{MSB}}{1} & 0 & 1 & 1 & 0 & 1 & 1 & \underset{\bold{LSB}}{0} \end{matrix} MSB 1 ​ ​ 0 ​ 1 ​ 1 ​ 0 ​ 1 ​ 1 ​ LSB 0 ​ ​

What are ASCII and extended ASCII encoding schemes ?

ASCII encoding scheme uses a 7-bit code and it represents 128 characters. Its advantages are simplicity and efficiency. Extended ASCII encoding scheme uses a 8-bit code and it represents 256 characters.

What is the utility of ISCII encoding scheme ?

ISCII or Indian Standard Code for Information Interchange can be used to represent Indian languages on the computer. It supports Indian languages that follow both Devanagari script and other scripts like Tamil, Bengali, Oriya, Assamese, etc.

What is Unicode ? What is its significance ?

Unicode is a universal character encoding scheme that can represent different sets of characters belonging to different languages by assigning a number to each of the character. It has the following significance:

• It defines all the characters needed for writing the majority of known languages in use today across the world.
• It is a superset of all other character sets.
• It is used to represent characters across different platforms and programs.

What all encoding schemes does Unicode use to represent characters ?

Unicode uses UTF-8, UTF-16 and UTF-32 encoding schemes.

What are ASCII and ISCII ? Why are these used ?

ASCII stands for American Standard Code for Information Interchange. It uses a 7-bit code and it can represent 128 characters. ASCII code is mostly used to represent the characters of English language, standard keyboard characters as well as control characters like Carriage Return and Form Feed. ISCII stands for Indian Standard Code for Information Interchange. It uses a 8-bit code and it can represent 256 characters. It retains all ASCII characters and offers coding for Indian scripts also. Majority of the Indian languages can be represented using ISCII.

What are UTF-8 and UTF-32 encoding schemes. Which one is more popular encoding scheme ?

UTF-8 is a variable length encoding scheme that uses different number of bytes to represent different characters whereas UTF-32 is a fixed length encoding scheme that uses exactly 4 bytes to represent all Unicode code points. UTF-8 is the more popular encoding scheme.

What do you understand by code point ?

Code point refers to a code from a code space that represents a single character from the character set represented by an encoding scheme. For example, 0x41 is one code point of ASCII that represents character 'A'.

What is the difference between fixed length and variable length encoding schemes ?

Variable length encoding scheme uses different number of bytes or octets (set of 8 bits) to represent different characters whereas fixed length encoding scheme uses a fixed number of bytes to represent different characters.

Type B: Application Based Questions

Convert the following binary numbers to decimal:

Equivalent decimal number = 1 + 4 + 8 = 13

Therefore, (1101) 2 = (13) 10

Equivalent decimal number = 2 + 8 + 16 + 32 = 58

Equivalent decimal number = 1 + 2 + 4 + 8 + 16 + 64 + 256 = 351

Convert the following binary numbers to decimal :

Equivalent decimal number = 4 + 8 = 12

(b) 10010101

(c) 11011100

Convert the following decimal numbers to binary:

Therefore, (0.25) 10 = (0.01) 2

Therefore, (122) 10 = (1111010) 2

(We stop after 5 iterations if fractional part doesn't become 0)

Therefore, (0.675) 10 = (0.10101) 2

Convert the following decimal numbers to octal:

Therefore, (122) 10 = (172) 8

Therefore, (0.675) 10 = (0.53146) 8

Convert the following hexadecimal numbers to binary:

(23D) 16 = (1000111101) 2

Convert the following binary numbers to hexadecimal:

(a) 1010110110111

(b) 10110111011011

(c) 0110101100

0001 undefined 1010 undefined 1100 undefined \underlinesegment{0001} \quad \underlinesegment{1010} \quad \underlinesegment{1100} 0001 ​ 1010 ​ 1100 ​

Therefore, (0110101100) 2 = (1AC) 16

Convert the following octal numbers to decimal:

Equivalent decimal number = 7 + 40 + 128 = 175

Therefore, (257) 8 = (175) 10

Equivalent decimal number = 7 + 16 + 320 + 1536 = 1879

Therefore, (3527) 8 = (1879) 10

Equivalent decimal number = 3 + 16 + 64 = 83

Therefore, (123) 8 = (83) 10

Integral part

Fractional part.

Equivalent decimal number = 5 + 384 + 0.125 + 0.0312 = 389.1562

Therefore, (605.12) 8 = (389.1562) 10

Convert the following hexadecimal numbers to decimal:

Equivalent decimal number = 6 + 160 = 166

Therefore, (A6) 16 = (166) 10

Equivalent decimal number = 11 + 48 + 256 + 40960 = 41275

Therefore, (A13B) 16 = (41275) 10

Equivalent decimal number = 5 + 160 + 768 = 933

Therefore, (3A5) 16 = (933) 10

Equivalent decimal number = 9 + 224 = 233

Therefore, (E9) 16 = (233) 10

Equivalent decimal number = 3 + 160 + 3072 + 28672 = 31907

Therefore, (7CA3) 16 = (31907) 10

Convert the following decimal numbers to hexadecimal:

Therefore, (132) 10 = (84) 16

Therefore, (2352) 10 = (930) 16

Therefore, (122) 10 = (7A) 16

Therefore, (0.675) 10 = (0.ACCCC) 16

Therefore, (206) 10 = (CE) 16

Therefore, (3619) 10 = (E23) 16

Convert the following hexadecimal numbers to octal:

(38AC) 16 = (11100010101100) 2

011 undefined   100 undefined   010 undefined   101 undefined   100 undefined \underlinesegment{011}\medspace\underlinesegment{100}\medspace\underlinesegment{010}\medspace\underlinesegment{101}\medspace\underlinesegment{100} 011 ​ 100 ​ 010 ​ 101 ​ 100 ​

(38AC) 16 = (34254) 8

(7FD6) 16 = (111111111010110) 2

111 undefined   111 undefined   111 undefined   010 undefined   110 undefined \underlinesegment{111}\medspace\underlinesegment{111}\medspace\underlinesegment{111}\medspace\underlinesegment{010}\medspace\underlinesegment{110} 111 ​ 111 ​ 111 ​ 010 ​ 110 ​

(7FD6) 16 = (77726) 8

(ABCD) 16 = (1010101111001101) 2

001 undefined   010 undefined   101 undefined   111 undefined   001 undefined   101 undefined \underlinesegment{001}\medspace\underlinesegment{010}\medspace\underlinesegment{101}\medspace\underlinesegment{111}\medspace\underlinesegment{001}\medspace\underlinesegment{101} 001 ​ 010 ​ 101 ​ 111 ​ 001 ​ 101 ​

(ABCD) 16 = (125715) 8

Convert the following octal numbers to binary:

Therefore, (123) 8 = ( 001 undefined   010 undefined   011 undefined \bold{\underlinesegment{001}}\medspace\bold{\underlinesegment{010}}\medspace\bold{\underlinesegment{011}} 001 ​ 010 ​ 011 ​ ) 2

Therefore, (3527) 8 = ( 011 undefined   101 undefined   010 undefined   111 undefined \bold{\underlinesegment{011}}\medspace\bold{\underlinesegment{101}}\medspace\bold{\underlinesegment{010}}\medspace\bold{\underlinesegment{111}} 011 ​ 101 ​ 010 ​ 111 ​ ) 2

Therefore, (705) 8 = ( 111 undefined   000 undefined   101 undefined \bold{\underlinesegment{111}}\medspace\bold{\underlinesegment{000}}\medspace\bold{\underlinesegment{101}} 111 ​ 000 ​ 101 ​ ) 2

Therefore, (7642) 8 = ( 111 undefined   110 undefined   100 undefined   010 undefined \bold{\underlinesegment{111}}\medspace\bold{\underlinesegment{110}}\medspace\bold{\underlinesegment{100}}\medspace\bold{\underlinesegment{010}} 111 ​ 110 ​ 100 ​ 010 ​ ) 2

Therefore, (7015) 8 = ( 111 undefined   000 undefined   001 undefined   101 undefined \bold{\underlinesegment{111}}\medspace\bold{\underlinesegment{000}}\medspace\bold{\underlinesegment{001}}\medspace\bold{\underlinesegment{101}} 111 ​ 000 ​ 001 ​ 101 ​ ) 2

Therefore, (3576) 8 = ( 011 undefined   101 undefined   111 undefined   110 undefined \bold{\underlinesegment{011}}\medspace\bold{\underlinesegment{101}}\medspace\bold{\underlinesegment{111}}\medspace\bold{\underlinesegment{110}} 011 ​ 101 ​ 111 ​ 110 ​ ) 2

Convert the following binary numbers to octal

111 undefined 010 undefined \underlinesegment{111} \quad \underlinesegment{010} 111 ​ 010 ​

Therefore, (111010) 2 = (72) 8

(b) 110110101

110 undefined 110 undefined 101 undefined \underlinesegment{110} \quad \underlinesegment{110} \quad \underlinesegment{101} 110 ​ 110 ​ 101 ​

Therefore, (110110101) 2 = (665) 8

(c) 1101100001

001 undefined 101 undefined 100 undefined 001 undefined \underlinesegment{001} \quad \underlinesegment{101} \quad \underlinesegment{100} \quad \underlinesegment{001} 001 ​ 101 ​ 100 ​ 001 ​

Therefore, (1101100001) 2 = (1541) 8

011 undefined 001 undefined \underlinesegment{011} \quad \underlinesegment{001} 011 ​ 001 ​

Therefore, (11001) 2 = (31) 8

(b) 10101100

010 undefined 101 undefined 100 undefined \underlinesegment{010} \quad \underlinesegment{101} \quad \underlinesegment{100} 010 ​ 101 ​ 100 ​

Therefore, (10101100) 2 = (254) 8

(c) 111010111

111 undefined 010 undefined 111 undefined \underlinesegment{111} \quad \underlinesegment{010} \quad \underlinesegment{111} 111 ​ 010 ​ 111 ​

Therefore, (111010111) 2 = (727) 8

Add the following binary numbers:

(i) 10110111 and 1100101

1 1 0 1 1 1 0 1 1 1 1 1 1 + 1 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 \begin{matrix} & & \overset{1}{1} & \overset{1}{0} & 1 & 1 & \overset{1}{0} & \overset{1}{1} & \overset{1}{1} & 1 \\ + & & & 1 & 1 & 0 & 0 & 1 & 0 & 1 \\ \hline & \bold{1} & \bold{0} & \bold{0} & \bold{0} & \bold{1} & \bold{1} & \bold{1} & \bold{0} & \bold{0} \end{matrix} + ​ 1 ​ 1 1 0 ​ 0 1 1 0 ​ 1 1 0 ​ 1 0 1 ​ 0 1 0 1 ​ 1 1 1 1 ​ 1 1 0 0 ​ 1 1 0 ​ ​

Therefore, (10110111) 2 + (1100101) 2 = (100011100) 2

(ii) 110101 and 101111

1 1 1 1 0 1 1 1 0 1 1 + 1 0 1 1 1 1 1 1 0 0 1 0 0 \begin{matrix} & & \overset{1}{1} & \overset{1}{1} & \overset{1}{0} & \overset{1}{1} & \overset{1}{0} & 1 \\ + & & 1 & 0 & 1 & 1 & 1 & 1 \\ \hline & \bold{1} & \bold{1} & \bold{0} & \bold{0} & \bold{1} & \bold{0} & \bold{0} \end{matrix} + ​ 1 ​ 1 1 1 1 ​ 1 1 0 0 ​ 0 1 1 0 ​ 1 1 1 1 ​ 0 1 1 0 ​ 1 1 0 ​ ​

Therefore, (110101) 2 + (101111) 2 = (1100100) 2

(iii) 110111.110 and 11011101.010

0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 . 1 1 1 0 + 1 1 0 1 1 1 0 1 . 0 1 0 1 0 0 0 1 0 1 0 1 . 0 0 0 \begin{matrix} & & \overset{1}{0} & \overset{1}{0} & \overset{1}{1} & \overset{1}{1} & \overset{1}{0} & \overset{1}{1} & \overset{1}{1} & \overset{1}{1} & . & \overset{1}{1} & 1 & 0 \\ + & & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & . & 0 & 1 & 0 \\ \hline & \bold{1} & \bold{0} & \bold{0} & \bold{0} & \bold{1} & \bold{0} & \bold{1} & \bold{0} & \bold{1} & \bold{.} & \bold{0} & \bold{0} & \bold{0} \end{matrix} + ​ 1 ​ 0 1 1 0 ​ 0 1 1 0 ​ 1 1 0 0 ​ 1 1 1 1 ​ 0 1 1 0 ​ 1 1 1 1 ​ 1 1 0 0 ​ 1 1 1 1 ​ . . . ​ 1 1 0 0 ​ 1 1 0 ​ 0 0 0 ​ ​

Therefore, (110111.110) 2 + (11011101.010) 2 = (100010101) 2

(iv) 1110.110 and 11010.011

0 1 1 1 1 1 1 0 1 . 1 1 1 0 + 1 1 0 1 0 . 0 1 1 1 0 1 0 0 1 . 0 0 1 \begin{matrix} & & \overset{1}{0} & \overset{1}{1} & \overset{1}{1} & 1 & \overset{1}{0} & . & \overset{1}{1} & 1 & 0 \\ + & & 1 & 1 & 0 & 1 & 0 & . & 0 & 1 & 1 \\ \hline & \bold{1} & \bold{0} & \bold{1} & \bold{0} & \bold{0} & \bold{1} & \bold{.} & \bold{0} & \bold{0} & \bold{1} \end{matrix} + ​ 1 ​ 0 1 1 0 ​ 1 1 1 1 ​ 1 1 0 0 ​ 1 1 0 ​ 0 1 0 1 ​ . . . ​ 1 1 0 0 ​ 1 1 0 ​ 0 1 1 ​ ​

Therefore, (1110.110) 2 + (11010.011) 2 = (101001.001) 2

Question 21

Given that A's code point in ASCII is 65, and a's code point is 97. What is the binary representation of 'A' in ASCII ? (and what's its hexadecimal representation). What is the binary representation of 'a' in ASCII ?

Binary representation of 'A' in ASCII will be binary representation of its code point 65.

Converting 65 to binary:

Therefore, binary representation of 'A' in ASCII is 1000001.

Converting 65 to Hexadecimal:

Therefore, hexadecimal representation of 'A' in ASCII is (41) 16 .

Similarly, converting 97 to binary:

Therefore, binary representation of 'a' in ASCII is 1100001.

Question 22

Convert the following binary numbers to decimal, octal and hexadecimal numbers.

(i) 100101.101

Decimal Conversion of integral part:

Decimal Conversion of fractional part:

Equivalent decimal number = 1 + 4 + 32 + 0.5 + 0.125 = 37.625

Therefore, (100101.101) 2 = (37.625) 10

Octal Conversion

100 undefined 101 undefined . 101 undefined \underlinesegment{100} \quad \underlinesegment{101} \quad \bold{.} \quad \underlinesegment{101} 100 ​ 101 ​ . 101 ​

Therefore, (100101.101) 2 = (45.5) 8

Hexadecimal Conversion

0010 undefined 0101 undefined   .   1010 undefined \underlinesegment{0010} \quad \underlinesegment{0101} \medspace . \medspace \underlinesegment{1010} 0010 ​ 0101 ​ . 1010 ​

Therefore, (100101.101) 2 = (25.A) 16

(ii) 10101100.01011

Equivalent decimal number = 4 + 8 + 32 + 128 + 0.25 + 0.0625 + 0.03125 = 172.34375

Therefore, (10101100.01011) 2 = (172.34375) 10

010 undefined 101 undefined 100 undefined . 010 undefined 110 undefined \underlinesegment{010} \quad \underlinesegment{101} \quad \underlinesegment{100} \quad \bold{.} \quad \underlinesegment{010} \quad \underlinesegment{110} 010 ​ 101 ​ 100 ​ . 010 ​ 110 ​

Therefore, (10101100.01011) 2 = (254.26) 8

1010 undefined 1100 undefined   .   0101 undefined   1000 undefined \underlinesegment{1010} \quad \underlinesegment{1100} \medspace . \medspace \underlinesegment{0101} \medspace \underlinesegment{1000} 1010 ​ 1100 ​ . 0101 ​ 1000 ​

Therefore, (10101100.01011) 2 = (AC.58) 16

Decimal Conversion:

Equivalent decimal number = 2 + 8 = 10

001 undefined 010 undefined \underlinesegment{001} \quad \underlinesegment{010} 001 ​ 010 ​

Therefore, (1010) 2 = (12) 8

(iv) 10101100.010111

Equivalent decimal number = 4 + 8 + 32 + 128 + 0.25 + 0.0625 + 0.03125 + 0.015625 = 172.359375

Therefore, (10101100.010111) 2 = (172.359375) 10

010 undefined 101 undefined 100 undefined . 010 undefined 111 undefined \underlinesegment{010} \quad \underlinesegment{101} \quad \underlinesegment{100} \quad \bold{.} \quad \underlinesegment{010} \quad \underlinesegment{111} 010 ​ 101 ​ 100 ​ . 010 ​ 111 ​

Therefore, (10101100.010111) 2 = (254.27) 8

1010 undefined 1100 undefined   .   0101 undefined   1100 undefined \underlinesegment{1010} \quad \underlinesegment{1100} \medspace . \medspace \underlinesegment{0101} \medspace \underlinesegment{1100} 1010 ​ 1100 ​ . 0101 ​ 1100 ​

Therefore, (10101100.010111) 2 = (AC.5C) 16

Teach Computer Science

KS3 Computer Science Data Representation Resources

Ks3 computer science data representation topics.

This module provides a strong base for your students’ computer science knowledge and allows you to teach the basic concepts of computer science. Including:

Module 32: Binary system Module 33: Hexadecimal system Module 34: Character sets Module 35: Images Module 36: Steganography Module 37: Sound Module 38: Compression Module 39: Encryption algorithms

What’s included?

Each module contains:

• An editable PowerPoint lesson presentation
• Editable revision handouts
• A glossary which covers the key terminologies of the module
• Topic mindmaps for visualising the key concepts
• Printable flashcards to help students engage active recall and confidence-based repetition
• A quiz with accompanying answer key to test knowledge and understanding of the module

As a premium member, you get access to the entire library of KS3 Computer science resources. Choose your modules to below to start your downloads.

Binary system

Download ks3 module 32: binary system.

This download is exclusively for Teach Computer Science subscribers! To download this file, click the button below to signup (it only takes a minute) and you'll be brought right back to this page to start the download!

Hexadecimal system

Download ks3 module 33: hexadecimal system, character sets, download ks3 module 34: character sets, download ks3 module 35: images.

Steganography

Download KS3 Module 36: Steganography

Download ks3 module 37: sound, compression, download ks3 module 38: compression, encryption algorithms, download ks3 module 39: encryption algorithms.

View All Modules

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KS3 Data and data representation

How does a computer store an image? What happens if we decrease the quality of an image file? Can we recreate the original image if we decrease its' quality? Are there ways to reduce the size of an audio file without losing the quality of the audio when it is played back?

Understanding data and how it is represented within the computer system can help students become better programmers and better able to understand the limitations of the data processing. Knowing that no matter how much an image is enhanced no extra details can be added, or that if an audio track is down sampled data is going to be lost are both fundamental to understanding. 

Data Representation: Bitmap Images

Quality Assured Category: Computing Publisher: Nichola Wilkin Ltd

A lesson plan and series of activities to help students understand that bitmapped images are built up purely of pixels. This includes a spreadsheet designed to represent monochrome and then simple colour images. The effect of increasing the range of colours available and its' effect on file size is discussed in some depth. 

Bitmap canvas editor in Excel

Quality Assured Category: Computing Publisher:

Although this resource does not contain any instructions for how to use it in a lesson, or lesson plans to go with it, it could easily be used to support the delivery of other activities as students learn about how images are created and stored, as well as how they are represented in the memory of a computer. Asking students to experiment with the images they are able to generate using this tool should give them a firmer grasp of how pixel data can be encoded in an image file

Binary and bitmapped images

A series of spreadsheet-based activities to simulate both binary and hexadecimal encoded image files. The students are required to convert between binary and hexadecimal as well as too and from denary as part of the process of solving these puzzles. The worksheet contains a number of example pictures which the students are required to recreate. There are a number of revised spreadsheet files each with slightly modified versions to enable different variants of the basic process to be undertaken by the students. 

Colour by Numbers - Image representation

Quality Assured Category: Computing Publisher: Computer Science Unplugged

A resource from CS Unplugged which looks at ways in which images can be represented by black and white pixels. It includes a number of activities to help students look at the way in which Run Length Encoding can be used to minimise the actual size of data which has to be transmitted by a fax machine (or stored on a disk). A discussion of the underlying ideas is included. 

Introduction to sound and music computing

A highly technical overview of how sound is represented in a computer, how digitising sound changes the quality of it and how reducing the sample rates can effect the resulting audio. The resource also comes with a number of sound samples to illustrate these concepts, along with both Python and Scratch programs to enable students to investigate further

Making data digital

This resource consists of a presentation which looks in various ways at how digital images and sounds are quantified in such a way that the computer can store and interpret them. This looks at the effects of digitising different types of data, and the effect that this has on both the size and the quality of the resulting files. It may be necessary to produce some supporting activities for students to undertake in lessons, to support their understanding of the content of this presentation. 

Count the Dots - Binary Numbers

An introduction to the binary number system, this activity from CS Unplugged explains the theories which underpin the use of base 2, as well as why and how computers use this as their fundamental building block. A series of activities are included to help consolidate students understanding of the binary system, and include discussion of how characters and other types of data can be encoded. 

Computational thinking and algorithms

Quality Assured Category: Computing Publisher: Computing At School

An unplugged activity to convert binary numbers into coordinates that enable students to recreate an image using values given in binary. The resource also includes a spreadsheet which can be used to make more complex images for use with students at a more advanced level. The presentation is more of a discussion of computational thinking and is not really relevant to this activity. Once students have completed the activity for themselves, they could be asked to create their own image in a similar way to the one they have recreated, and generate a coordinate list for their image in binary. The discussions listed in the activity sheet should also be useful to broaden students understanding of the use of binary as well as how it might be possible to speed up a computer system in similar situations. 

You Can Say That Again! - Text Compression

Reducing the amount of space that information occupies in a computer memory can make it easier to store more data, this activity from CS Unplugged looks at how text can be compressed so that no information is lost, but the overall file size can be significantly reduced. A series of activities to consolidate these ideas are presented along with an in depth discussion of what is going on in terms of the underlying computer science. 

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DATA REPRESENTATION (Worksheet)

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IGCSE Computer Science Chapter 1 - Data Representation [174x Animated Slide+PYQ]

Subject: Computing

Age range: 14-16

Resource type: Lesson (complete)

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Complete IGCSE Computer Science [Chapter 1 - Data Representation] teaching/revision slides (2023 - 2025 syllabus)

Topic included: Chapter 1.1 - Number System (Denary, Binary and Hexadecimal conversion) Chapter 1.2 - Usage of Hexadecimal System Chapter 1.3 - Addition of binary numbers Chapter 1.4 - Binary Shifting (Multiplication and division of binary numbers) Chapter 1.5 - Two’s complement (Representing negative number in binary) Chapter 1.6 - How text, sound and images are represented in binary Chapter 1.7 - Measurement of Data Storage and Calculation of File Size Chapter 1.8 - Data Compression

Features of the slides: Feature 1 - Animated PPT Feature 2 - DIY (Do it yourself) session for students to practice what they just learned Feature 3 - Carefully slides using Canva to improve students’ engagement Feature 4 - Details step-by-step explanation (A textbook is not required) Feature 5 - Past year questions for students to practice for the IGCSE exam

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⭐️ [Slides + Topical PYQ] IGCSE Computer Science FULL CURRICULUM (2023-2025)

Introducing an invaluable time-saving solution! Discover our meticulously crafted bundle of high school Computer Science slides, designed to enhance the learning experience for both you and your students. As an experienced educator, James, I have dedicated over 200 hours to curating this comprehensive collection, ensuring optimal engagement and improved academic outcomes. When you purchase this exceptional bundle, you gain access to a wealth of professionally designed slides that cover the entire IGCSE 2023-2025 syllabus for Computer Science. Each chapter is thoughtfully organized and meticulously animated to captivate your students' attention while fostering a deeper understanding of the subject matter. Let's explore the extensive chapters included in this bundle: 1. Chapter 1 – Data Representation (174 slides) 2. Chapter 2 – Data Transmission (108 slides) 3. Chapter 3 – Hardware (275 slides) 4. Chapter 4 – Software (128 slides) 5. Chapter 5 – Internet and the World Wide Web (179 slides) 6. Chapter 6 – Automated System (A.I) (87 slides) 7. Chapter 7 – Algorithm and Problem Solving (182 slides) 8. Chapter 8 – Programming with Python and Pseudocode (200 slides) 9. Chapter 9 – Databases (53 slides) 10. Chapter 10 – Logic Gates (117 slides) The features of these slides are tailored to maximize student engagement and understanding: 1. Engaging Visuals: Our slides don't rely solely on words; they incorporate captivating images to keep your class fully engaged throughout each lesson. 2. Enhanced Comprehension: The animated elements integrated into the slides enhance student comprehension, allowing complex concepts to be grasped more easily. 3. Aesthetic Design: These slides are meticulously crafted using a beautiful color palette, ensuring an appealing visual experience that complements the educational content. Additionally, we have gone the extra mile to provide you with supplementary materials. This bundle includes worksheets for Chapters 1 to 5, 7, 9, and 10. These self-made worksheets consist of topical past-year questions from 2019 to 2022, accompanied by comprehensive answers, giving your students valuable practice and reinforcement. Contact me (find my email at profile) if you have any query. Don't miss out on this time-saving opportunity to revolutionize your Computer Science lessons. Invest in our meticulously curated bundle of slides today and witness the transformation in your classroom's engagement and academic success.

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CBSE Worksheets for Class 11 Computer Science

CBSE Worksheets for Class 11 Computer Science: One of the best teaching strategies employed in most classrooms today is Worksheets. CBSE Class 11 Computer Science Worksheet for students has been used by teachers & students to develop logical, lingual, analytical, and problem-solving capabilities. So in order to help you with that, we at WorksheetsBuddy have come up with Kendriya Vidyalaya Class 11 Computer Science Worksheets for the students of Class 11. All our CBSE NCERT Class 11 Computer Science practice worksheets are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance. These chapter wise test papers for Class 11 Computer Science will be useful to test your conceptual understanding.

Board: Central Board of Secondary Education(www.cbse.nic.in) Subject: Class 11 Computer Science Number of Worksheets: 20

CBSE Class 11 Computer Science Worksheets PDF

All the CBSE Worksheets for Class 11 Computer Science provided in this page are provided for free which can be downloaded by students, teachers as well as by parents. We have covered all the Class 11 Computer Science important questions and answers in the worksheets which are included in CBSE NCERT Syllabus. Just click on the following link and download the CBSE Class 11 Computer Science Worksheet. CBSE Worksheets for Class 11 Computers can also use like assignments for Class 11 Computer Science students.

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• CBSE Worksheets for Class 11 Computer Science Assignment 1
• CBSE Worksheets for Class 11 Computer Science Assignment 2
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• CBSE Worksheets for Class 11 Computer Science Assignment 7
• CBSE Worksheets for Class 11 Computer Science Assignment 8
• CBSE Worksheets for Class 11 Computer Science Assignment 9

Advantages of CBSE Class 11 Computer Science Worksheets

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Worksheets of CBSE Class 11 Computer Science are devised by experts of WorksheetsBuddy experts who have great experience and expertise in teaching Maths. So practising these worksheets will promote students problem-solving skills and subject knowledge in an interactive method. Students can also download CBSE Class 11 Computer Science Chapter wise question bank pdf and access it anytime, anywhere for free. Browse further to download free CBSE Class 11 Computer Science Worksheets PDF .

Now that you are provided all the necessary information regarding CBSE Class 11 Computer Science Worksheet and we hope this detailed article is helpful. So Students who are preparing for the exams must need to have great solving skills. And in order to have these skills, one must practice enough of Class 11 Computers revision worksheets . And more importantly, students should need to follow through the worksheets after completing their syllabus.  Working on CBSE Class 11 Computer Science Worksheets will be a great help to secure good marks in the examination. So start working on Class 11 Computers Worksheets to secure good score.

CBSE Worksheets For Class 11

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