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.
Reviewed by: AI editorial process; not yet individually human-reviewed
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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 to hexadecimal. [1 mark]
- Cue. , , so .
Q2. Convert the hexadecimal value to denary. [1 mark]
- Cue. .
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.Show worked answer →
Split the 8 bits into two nibbles of 4 bits: and .
Convert each nibble using place values : , which is C in hexadecimal; , which is A in hexadecimal.
Join the two hex digits: .
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.Show worked answer →
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 and . The digit 2 is in the 16s column () and F is 15 in the units column (). .
Markers reward two valid reasons and the correct conversion with working ().
Related dot points
- Converting between denary and binary (up to and including 8 bits), binary addition and the detection of overflow, and binary shifts and their effect.
An OCR J277 1.2.4 answer on converting between denary and binary up to 8 bits, adding binary numbers and detecting overflow, and binary shifts and their effect on a value.
- Why data must be represented in binary, the units of information (bit, nibble, byte, kB, MB, GB, TB, PB) and how to convert between them.
An OCR J277 1.2.3 answer on why computers use binary, the units of information from bit and nibble up to petabyte, and how to convert between units of data capacity.
- Representing characters with ASCII and Unicode; representing images with pixels, colour depth, resolution and metadata; representing sound with sample rate, sample resolution and bit rate; and the effect on file size and quality.
An OCR J277 1.2.4 answer on representing characters (ASCII, Unicode), images (pixels, colour depth, resolution, metadata) and sound (sample rate, sample resolution, bit rate), and the effect of each on file size and quality.
- The need for primary storage, the purpose and characteristics of RAM and ROM, the differences between them, and the need for virtual memory.
An OCR J277 1.2.1 answer on the need for primary storage, the purpose and characteristics of RAM and ROM, the differences between them, and why virtual memory is needed.
- The need for compression and the difference between lossy and lossless compression, with their typical uses.
An OCR J277 1.2.5 answer on the need for data compression and the difference between lossy and lossless compression, including how each works and their typical uses.
Sources & how we know this
- OCR GCSE (9-1) Computer Science (J277) specification — OCR (2020)