Number Systems (CIE IGCSE Computer Science)

Topic Questions

1a
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4 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.

a)
Complete the binary register for these two pairs of digits.

97                


5C                
[4]
1b
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2 marks
b)
Give two other uses of hexadecimal in computer science.

1 ..................................................................
2 ...................................................................
[2]
1c
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2 marks
c)
Another value is stored as binary in a register.

0 1 0 1 0 0 1 0

i)
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.

               
[1]
ii)
State one effect this logical shift has on the binary value.
 [1]
1d
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2 marks
d)
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.

Working space ...........................................


Register:                

[2]

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2
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2 marks

Benedict has a computer that is assigned an Internet Protocol (IP) address. The IP address is:

198.167.214.0

The IP address is represented as denary values.

Convert the denary values 167 and 214 from the IP address to 8-bit binary.

167                

214                

Working space ...............................................................

[2]

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3
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6 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    

[6]

Working space .........................................

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4
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6 marks

Tina is creating a website for charity events. She uses HTML to create the website.

She uses the hexadecimal colour code #43B7F0 as the background colour for her website. 

The hexadecimal colour code #43B7F0 is stored in three 8-bit registers.

Give the
8-bit binary values for each part of the hexadecimal code.



43                

B7                

F0                

[6]

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5a
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4 marks
Ina)
Four denary to 8-bit binary conversions are given.

 Tick () to show if each denary to 8-bit binary conversion is Correct or Incorrect.

Denary Binary Conversion Correct 
(✓)
Incorrect 
(✓)
145 10010001    
179 10110101    
11 00010011    
100 01100010    

[4]

5b
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3 marks
b)
Convert the 12-bit binary number into hexadecimal.

1 1 0 0 0 1 0 0 0 0 0 0

[3]

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6a
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2 marks

A digital alarm clock is controlled by a microprocessor. It uses the 24-hour clock system (i.e. 6 pm is 18:00).

Each digit in a typical display is represented by a 4-digit binary code.

For example:q4-paper1-spec2019-cie-igcse-computerscience

a)
What time is shown on the clock display if the 4-digit binary codes are:
q4a-paper1-spec2019-cie-igcse-computerscience

[2]

6b
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4 marks
b)
What would be stored in the 4-digit binary codes if the clock display time was:

q4b-paper1-spec2019-cie-igcse-computerscience
[4]

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7a
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4 marks

When a key is pressed on the keyboard, the computer stores the ASCII representation of the character typed into main memory.

The ASCII representation for A is 65 (denary), for B is 66 (denary), etc.

There are two letters stored in the following memory locations:

Location 1  A
Location 2  C


a)

i)
Show the contents of Location 1 and Location 2 as binary using 8 bits.

Location 1                

.
Location 2                



ii)
[2]

Show the contents of Location 1 and Location 2 as hexadecimal.

Location 1 ...............................................
Location 2 ...............................................
[2]
7b
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4 marks
b)
The following machine code instruction is stored in a location of main memory:

1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1

Convert this binary pattern into hexadecimal.

[4]

7c
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2 marks
c)
Explain why a programmer would prefer to see the contents of the locations displayed as hexadecimal rather than binary, when debugging his program that reads the key presses.

[2]

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