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Binary, denary and hexadecimal

OCR GCSE Computer Science (J277) · Computer systems (Paper 1) › Memory and storage › Data storage

Practise Binary, denary and hexadecimal. 12 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.

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State the denary place value of the most significant bit in an 8-bit binary number.
128
State the largest 2-digit hexadecimal number and give its denary value.
FF = 255
State how many bits are needed to represent one hexadecimal digit.
4

Sample questions

Written for this site in the style of OCR exam questions. They are not taken from real past papers.

Question 1Easy3 marks
(a) State the denary place value of the most significant bit in an 8-bit binary number.[1]
(b) Convert the binary number 00101101 into denary.[1]
(c) State the largest denary number that can be represented using 8 bits.[1]
Show the answer and mark scheme
(a) Answer: 128
  • 128
(b) Answer: 45
  • 45
(c) Answer: 255
  • 255
Question 2Medium3 marks
(a) Explain why hexadecimal is often used to represent binary values.[2]
(b) Give one example of where hexadecimal is used in computing.[1]
Show the answer and mark scheme
(a)
  • hexadecimal is shorter / uses fewer digits (one hex digit for every four bits)
  • it is easier for humans to read, remember and write
  • fewer mistakes are made when copying or typing it
  • it is easy to convert between hexadecimal and binary
(b)
  • colour codes (e.g. in HTML / CSS) / MAC addresses / IPv6 addresses / memory addresses / error codes
Question 3Hard4 marks
(a) Explain why each hexadecimal digit can be represented by exactly four binary digits.[2]
(b) Convert the binary number 1011100 into hexadecimal.
Show your working.[2]
Show the answer and mark scheme
(a)
  • there are 16 hexadecimal digits (0 to 9 and A to F)
  • four bits give 24 = 16 different patterns, so each hex digit matches exactly one 4-bit pattern (nibble)
(b) Answer: 5C
  • splits the bits into groups of four from the right / writes it as 8 bits: 0101 1100
  • 5C

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