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AQA GCSE CS · 3.3.1 to 3.3.2

Number Bases and Units of Information

Section A: 10 multiple choice questions, 10 marks. Section B: 5 written questions, 12 marks. Total 22 marks.

Name

Class

Date

Mark  / 22

Section A

Circle the letter of the correct answer. One mark each.

  1. 1Convert 10011010 into denary.1
    1. A146
    2. B154
    3. C156
    4. D158
  2. 2Convert 200 into 8 bit binary.1
    1. A10011000
    2. B11000100
    3. C11001000
    4. D11010000
  3. 3Convert 11101011 into hexadecimal.1
    1. AEB
    2. BD11
    3. CBE
    4. DE11
  4. 4Convert hexadecimal 3C into denary.1
    1. A48
    2. B56
    3. C60
    4. D62
  5. 5How many bits are there in a nibble?1
    1. A2
    2. B4
    3. C8
    4. D16
  6. 6Using AQA's convention, how many bytes are in 3 kilobytes?1
    1. A1024
    2. B3000
    3. C3072
    4. D24000
  7. 7Why do computers use binary rather than denary?1
    1. ABinary numbers are shorter than denary ones
    2. BDenary cannot represent negative numbers
    3. CBinary uses less electricity than any other base
    4. DTheir components have two easily distinguishable states, which is reliable
  8. 8Why is hexadecimal used to write memory addresses?1
    1. AMemory addresses cannot be written in binary
    2. BHexadecimal uses less memory than binary
    3. CHexadecimal is what the processor actually stores
    4. DOne hex digit represents exactly four bits, so values are shorter and easier to read
  9. 9A file is 4500000 bits. What is its size in megabytes, using AQA's convention?1
    1. A0.5625 MB
    2. B0.5369 MB
    3. C4.5 MB
    4. D5.625 MB
  10. 10What is the largest denary value that can be stored in one byte?1
    1. A127
    2. B128
    3. C255
    4. D256

Section B

Answer in the space provided. The number of marks tells you how many separate points to make.

  1. 1ExplainExplain why computers use the binary number system.2
  2. 2ConvertConvert the denary number 214 into 8 bit binary. Show your working.2
  3. 3ConvertConvert the binary number 01111010 into hexadecimal. Show your working.2
  4. 4ExplainExplain why programmers often write binary values in hexadecimal.3
  5. 5CalculateA file is 6 megabytes in size. Calculate how many bits this is, using 1 kilobyte as 1000 bytes.3

Mark scheme

Section A

1B2C3A4C5B6B7D8D9A10C

Section B

1 Explain why computers use the binary number system. 2

One mark for each of the following, to a maximum of 2.

  • The components a computer is built from have two distinguishable states
  • This makes storing and transmitting data reliable even when the signal degrades

Model answer. Computers are built from components such as transistors that have two clearly distinguishable states, either conducting or not conducting. Representing data with just two symbols means a value can still be read correctly even when the signal has been weakened or has picked up interference, which makes storage and transmission far more reliable than a system with many states would be.

2 Convert the denary number 214 into 8 bit binary. Show your working. 2

One mark for each of the following, to a maximum of 2.

  • Shows a valid method, such as subtracting place values
  • Gives the answer 11010110

Model answer. Starting from the largest place value, 128 fits into 214 leaving 86, so the 128 column is 1. 64 fits into 86 leaving 22, so 1. 32 does not fit, so 0. 16 fits into 22 leaving 6, so 1. 8 does not fit, so 0. 4 fits leaving 2, so 1. 2 fits leaving 0, so 1. Then 0. The answer is 11010110.

3 Convert the binary number 01111010 into hexadecimal. Show your working. 2

One mark for each of the following, to a maximum of 2.

  • Splits into two groups of four bits, 0111 and 1010
  • Gives the answer 7A

Model answer. Splitting the eight bits into groups of four from the right gives 0111 and 1010. The group 0111 is 4 plus 2 plus 1, which is 7. The group 1010 is 8 plus 2, which is 10, and 10 is written as A in hexadecimal. So the answer is 7A.

4 Explain why programmers often write binary values in hexadecimal. 3

One mark for each of the following, to a maximum of 3.

  • One hexadecimal digit represents exactly four bits
  • So a value can be written in a quarter of the characters
  • Shorter values are easier for people to read and less likely to be mistyped

Model answer. Sixteen is two to the power of four, so each hexadecimal digit corresponds to exactly four bits and a byte is always written as two hexadecimal digits. A long run of ones and zeros is extremely easy to lose your place in, and a single misread digit gives a completely different value. Written in hexadecimal the same value takes a quarter of the characters, so it is quicker to read aloud, quicker to write down and far easier to compare with another value, which is why memory addresses, colour codes and MAC addresses are all written this way.

5 A file is 6 megabytes in size. Calculate how many bits this is, using 1 kilobyte as 1000 bytes. 3

One mark for each of the following, to a maximum of 3.

  • Converts megabytes to kilobytes by multiplying by 1000
  • Converts kilobytes to bytes by multiplying by 1000
  • Multiplies bytes by 8 to get 48000000 bits

Model answer. Six megabytes is 6 times 1000, which is 6000 kilobytes. That is 6000 times 1000, which is 6000000 bytes. Each byte is 8 bits, so the file is 6000000 times 8, which is 48000000 bits.