Knowledge Organiser: Binary and Hexadecimal
This topic summary covers Knowledge Organiser: Binary and Hexadecimal within Binary & Hex for GCSE Computer Science. Revise Binary & Hex in Memory & Storage for GCSE Computer Science with 15 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 15 of 15 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 15 of 15
Practice
15 questions
Recall
22 flashcards
Knowledge Organiser: Binary and Hexadecimal
Key Terms
- Binary: Base 2 number system using only 0s and 1s
- Denary/Decimal: Base 10 number system (everyday counting)
- Hexadecimal: Base 16 number system using 0-9 and A-F
- Bit: A single binary digit (0 or 1)
- Nibble: 4 bits (represents exactly one hex digit)
- Byte: 8 bits (two hex digits)
- MSB: Most Significant Bit (leftmost, highest place value)
Must-Know Facts
- 8-bit binary place values: 128, 64, 32, 16, 8, 4, 2, 1
- Hex letters: A=10, B=11, C=12, D=13, E=14, F=15
- 1 hex digit = exactly 4 binary bits
- 8-bit range: 0 to 255 (00 to FF in hex)
- Hex is used for: memory addresses, colour codes (#FF5733), MAC addresses
- To convert binary to hex: group into 4-bit nibbles from the right
- To convert hex to binary: expand each digit to 4 bits (pad with leading 0s)
Key Concepts
- Binary to denary: Add place values where bit = 1 (e.g. 1011 = 8+2+1 = 11)
- Denary to binary: Find largest fitting place value, subtract and repeat
- Binary to hex: Group in 4s, convert each group (1101 0110 = D6)
- Hex to binary: Each hex digit becomes 4 bits (3A = 0011 1010)
- Hex to denary: Multiply each digit by its 16n place value (3F = 48+15 = 63)
- Why hex? Shorthand for binary — more compact and readable for humans
Common Mistakes
- Forgetting to pad hex digits to 4 bits: Each hex digit must expand to exactly 4 binary bits — 3 must become 0011, not just 11
- Wrong place values in binary: The 8-bit place values are 128, 64, 32, 16, 8, 4, 2, 1 — students often mix up the order or miss the 128 column
- Confusing hex letters with denary values: A=10, B=11, C=12, D=13, E=14, F=15 — forgetting that F represents 15, not 6
- Not grouping from the right when converting binary to hex: Always split binary into groups of 4 starting from the RIGHT (least significant end), padding with zeros on the left if needed
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Practice Questions for Binary & Hex
Which of the following correctly describes the hexadecimal number system?
Explain why hexadecimal is used instead of binary when programmers write memory addresses and colour codes. Give three reasons.
Quick Recall Flashcards
15 questions on Binary & Hex — practise free
Instant marking, adaptive difficulty, and 22 spaced repetition flashcards. Free until your GCSEs.
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