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Why is hexadecimal used and how do you convert between binary, denary and hex?

Why hexadecimal is used to represent numbers, and how to convert between binary, denary and hexadecimal.

An OCR J277 1.2.4 answer on why hexadecimal is used in computing and how to convert between binary, denary and hexadecimal, with worked conversions in both directions.

Generated by Claude Opus 4.89 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

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  1. What this dot point is asking
  2. Why hexadecimal is used
  3. Binary to hexadecimal and back
  4. Hexadecimal and denary
  5. Try this

What this dot point is asking

OCR wants you to say why hexadecimal is used in computing and to convert fluently between binary, denary and hexadecimal in both directions. The conversions are common Paper 1 questions, and the fastest route nearly always uses the fact that one hex digit equals exactly one 4-bit nibble.

Why hexadecimal is used

Hexadecimal appears in colour codes (for example a web colour like #FF8800), memory addresses and error codes, precisely because it compresses binary into a human-friendly form without losing the direct link to the bits.

Binary to hexadecimal and back

Hexadecimal and denary

Try this

Q1. Convert the binary number 1111000011110000 to hexadecimal. [1 mark]

  • Cue. 1111=F1111 = \text{F}, 0000=00000 = 0, so F0\text{F0}.

Q2. Convert the hexadecimal value 1A1A to denary. [1 mark]

  • Cue. 1×16+10=261 \times 16 + 10 = 26.

Q3. Give one reason hexadecimal is used instead of binary. [1 mark]

  • Cue. It is more concise and easier for people to read, write and check, with fewer copying errors, and each digit maps to a nibble.

Exam-style practice questions

Practice questions written in the style of OCR exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

OCR 20203 marksConvert the 8-bit binary number 11001010 into hexadecimal. Show your working.
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Split the 8 bits into two nibbles of 4 bits: 11001100 and 10101010.

Convert each nibble using place values 8,4,2,18, 4, 2, 1: 1100=8+4=121100 = 8 + 4 = 12, which is C in hexadecimal; 1010=8+2=101010 = 8 + 2 = 10, which is A in hexadecimal.

Join the two hex digits: CA\text{CA}.

Markers reward splitting into nibbles, converting each correctly, and using the letters A to F for 10 to 15. Converting the whole byte to denary first (202) and then to hex is also acceptable if done correctly.

OCR 20234 marksState two reasons why hexadecimal is used in computing, and convert the hexadecimal value 2F into denary. Show your working.
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Reasons (one mark each, up to two): hexadecimal is more concise than binary, so long binary numbers are shorter and easier for people to read and write; it is easier to spot errors and to convert, because each hex digit maps exactly to a 4-bit nibble; and it is less prone to human mistakes than copying long strings of 1s and 0s.

Convert 2F to denary: the place values are 1616 and 11. The digit 2 is in the 16s column (2×16=322 \times 16 = 32) and F is 15 in the units column (15×1=1515 \times 1 = 15). 32+15=4732 + 15 = 47.

Markers reward two valid reasons and the correct conversion with working (2×16+15=472 \times 16 + 15 = 47).

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