IGCSEComputer ScienceCambridge (CIE)Topic Questions1. Data RepresentationNumber Systems

Number Systems (Cambridge (CIE) IGCSE Computer Science)

Topic Questions

1 hour12 questions

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Number Systems

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1a1 mark

Binary is a number system used by computers.

Four 8-bit binary values are given.

Tick (✓) one box to show which 8-bit binary value is the correct conversion for the denary value 50.

  • 00101010

  • 00110010

  • 01001100

  • 01010000

Choose your answer

1b1 mark

Four 8-bit binary values are given.

Tick (✓) one box to show which 8-bit binary value is the correct conversion for the hexadecimal value 90.

  • 00001001

  • 01011010

  • 10010000

  • 01100100

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1c2 marks

Explain why a computer system can only process data in binary form

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1d3 marks

Two 8-bit binary values are given.

Add the two 8-bit binary values.

Give your answer in binary. Show all your working.

space space space space space 0 space 0 space 1 space 1 thin space 1 space 0 space 0 space 1 plus space 0 space 1 space 0 space 0 space 1 space 0 space 1 space 0 stack space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space with bar on top

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2a2 marks

All data needs to be converted to binary data so that it can be processed by a computer.

Explain why a computer can only process binary data.

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2b3 marks

The denary values 64, 101 and 242 are converted to 8‑bit binary values.

Give the 8‑bit binary value for each denary value.

64 ................................

101 ................................

242 ................................

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2c4 marks

The hexadecimal values 42 and CE are converted to binary.

Give the binary value for each hexadecimal value.

42 .................

CE ..................

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3a3 marks

Denary values are converted to binary values to be processed by a computer.

Draw one line from each denary value to the correctly converted 8‑bit binary value.

Table showing denary numbers 41, 174, and 86 paired with their corresponding 8-bit binary equivalents 00100001, 10100110, 00101001, 10000110, 10101110, and 01010110.

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3b2 marks

Binary values can also be converted to denary values.

Give the correct denary value for the 12‑bit binary value 000101010111

Show all your working.

Denary value ..........................................................

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42 marks

Hexadecimal is used for Hypertext Markup Language (HTML) colour codes.

An HTML colour code is:

#2F15D6

HTML colour codes and Media Access Control (MAC) addresses are two examples of where hexadecimal is used in Computer Science.

Give two other examples of where hexadecimal can be used in Computer Science.

Example 1

Example 2

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5a4 marks

A school network has several computers.

Each computer in the network has a media access control (MAC) address.

Hexadecimal is used for MAC addresses.

Part of a MAC address is given.

97–5C–E1


Each pair of digits is stored as binary in an 8-bit register.

Complete the binary register for these two pairs of digits.

97

 

 

 

 

 

 

 

 

5C

 

 

 

 

 

 

 

 

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5b2 marks

Give two other uses of hexadecimal in Computer Science.

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5c2 marks

Another value is stored as binary in a register.

0

1

0

1

0

0

1

0

A logical left shift of two places is performed on the binary value.

Complete the binary register to show its contents after this logical left shift.

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5d1 mark

State one effect this logical shift has on the binary value.

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6a1 mark

Binary is a number system used by computers.

Tick (✓) one box to show which statement about the binary number system is correct.

  • It is a base 1 system

  • It is a base 2 system

  • It is a base 10 system

  • It is a base 16 system

Choose your answer

6b3 marks

Denary numbers are converted to binary numbers to be processed by a computer.

Convert these three denary numbers to 8‑bit binary numbers.

50 ...............................

102 ..............................

221 ...............................

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6c3 marks

Two 8‑bit binary numbers are given.

Add the two 8‑bit binary numbers using binary addition.

Give your answer in binary. Show all your working.

Error converting from MathML to accessible text.

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12 marks

Negative denary numbers can also be represented as binary using two’s complement.

Complete the binary register for the denary value −54.

You must show all your working.

Register:

 

 

 

 

 

 

 

 

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23 marks

Binary is a number system used by computers.

Two 8-bit binary values are added.

The result of this calculation needs to be stored in an 8-bit register.

The denary result of this calculation is 301.

This generates an error

State the name of this type of error and explain why this error occurs.

Error name:

Explanation:

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32 marks

Two binary numbers are added by a computer and an overflow error occurs.

Explain why the overflow error occurred.

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46 marks

Hexadecimal is used for Hypertext Markup Language (HTML) colour codes.

An HTML colour code is:

#2F15D6

Each pair of digits is stored as binary in an 8‑bit register.

Give the 8‑bit binary value that would be stored for each pair of hexadecimal digits.

2F

15

D6

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52 marks

Binary numbers are stored in registers.

Negative denary numbers can be represented as binary using two’s complement.

Complete the binary register for the denary number –78

You must show all your working.

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16 marks

Ron is attending a music concert. He has bought three tickets.

Each ticket number is displayed as a hexadecimal number. 

Complete the table to show the 12-bit binary values and the denary values for each Hexadecimal ticket number

Hexadecimal 
ticket number

12-bit binary value

Denary value

028

 

 

1A9

 

 

20c

 

 

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