Hexadecimal, the nibble ↔ hex-digit mapping, and all four conversion directions. Seven stages from theory to mastery. Click any stage card to dive in — or continue where you left off.
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Hexadecimal is base-16 — a compact, human-readable shorthand for binary. Master the nibble ↔ hex digit mapping, four conversion directions, and the traps that cost marks every session.
Hexadecimal (hex) is a base-16 number system that computer scientists use as a compact, human-readable way to write binary. Instead of reading a 32-bit MAC address like 01001010 00011011 10001100 00111101, you read it as 4A:1B:8C:3D. Same data, half the digits, far fewer mistakes.
Cambridge want you to convert between binary, denary, and hex fluently — and to explain why we use hex without slipping into the classic wrong answers. The Nibble Splitter interactive gives you the mental model: every hex digit maps to exactly 4 bits.
| Term | Definition |
|---|---|
| Hexadecimal (hex) | A base-16 number system using digits 0–9 and letters A–F. |
| Base 16 | Each column is worth 16× the column to its right (16⁰=1, 16¹=16, 16²=256). |
| Hex digit | A single hex character (0–9 or A–F). One hex digit = one nibble = 4 bits. |
| Nibble | A group of 4 bits. Every nibble maps to exactly one hex digit. |
| MSN / LSN | Most / Least Significant Nibble. In a byte, the MSN is the left 4 bits, LSN is the right 4 bits. |
| MAC address | A hardware identifier written in hex, e.g. 4A:1B:8C:3D:2E:7F. |
| Memory address | The location of a value in memory, displayed in hex for readability. |
| Colour code | An HTML/CSS colour written as #RRGGBB where each pair is 00–FF (0–255 denary). |
| Quotient | The whole-number result of a division — used first when converting denary→hex. |
| Remainder | What's left after division — used second when converting denary→hex. |
| Column | Left digit (MSN) | Right digit (LSN) |
|---|---|---|
| Place value | 16¹ = 16 | 16⁰ = 1 |
| Range | 0 × 16 = 0 → F × 16 = 240 | 0 × 1 = 0 → F × 1 = 15 |
| 2-digit max | FF = (15 × 16) + (15 × 1) = 240 + 15 = 255 | |
| Bit count | Nibbles | Hex digits | Max value |
|---|---|---|---|
| 4 bits | 1 | 1 | F (15) |
| 8 bits | 2 | 2 | FF (255) |
| 12 bits | 3 | 3 | FFF (4095) |
| 16 bits | 4 | 4 | FFFF (65535) |
Convert the 8-bit binary number 11001010 to hexadecimal.
Convert the hex number 2F to denary.
Convert the denary number 236 to hex.
The computer still stores everything in binary. Hex is a human-readable shorthand. Never write "hex uses less memory" — that scores zero.
Cited: 2024 Mar examiner reportWhen you divide denary by 16, the quotient is the LEFT digit and the remainder is the RIGHT digit. 236 = 14 rem 12 → E then C → EC. Many candidates flip it to CE.
Cited: 2024 M/J examiner report — "some candidates gave the correct values but in the incorrect order, that is, CE instead of EC"Recurring trap. If the question says "convert to hexadecimal", the answer must be hex. Converting to binary loses the mark even if the binary is correct.
Cited: 2024 examiner report — "many candidates converted the denary numbers into binary rather than hexadecimal. Candidates must pay close attention to the wording of the question"If a nibble converts to 0, you must still write 0. Don't skip it. 00001101 is 0D, not just D.
Mark-scheme requires the benefit to be for humans: shorter, easier to read, less error-prone, easier to debug. "Computers process hex faster" or "hex uses fewer gates" scores zero.
Cited: 2024 Nov examiner reportIf the question asks for differences between binary and hex, describe both sides. "Hex uses 0–9 and A–F" alone is half an answer — you also need "binary uses only 0 and 1".
Cited: 2024 Nov examiner reportThese are the exact phrasings Cambridge accept. Learn them.
Answer these in your head, then tap to see the model answer. Aim for 5 or 6 right before moving on.
Hexadecimal uses 16 symbols: digits 0–9 and letters A–F. Base-16 means each column is worth 16× the one to its right.
Each hex digit maps to exactly 4 bits (one nibble). So 8 bits = 2 hex digits. 12 bits = 3 hex digits. Divide bit-count by 4.
Hex is a human-readable shorthand. The computer still stores binary. Never write "hex saves storage" — that's the classic wrong answer.
Hex does NOT take less memory or storage than binary. It is a human-readable shorthand only. The computer still stores everything in binary.
Cited: 2024 Mar examiner report• Shorter and easier to read
• Less likely to make transcription mistakes
• Easier to spot errors and debug
• Takes up less screen space
• Debugging — memory addresses, error codes
• MAC addresses — e.g. 4A:1B:8C:3D:2E:7F
• Colour codes — e.g. #FF5733
• Assembly language — values in hex
Benefits must reference HUMANS. Never say hex is faster for the computer or uses fewer logic gates. Both are wrong.
Cited: 2024 Nov examiner reportClick each bit to toggle it. Watch how the 8 bits split into two nibbles, and each nibble live-converts to a hex digit. This is the mental model that makes every hex conversion instant.
Split into nibbles from the right. Convert each nibble to its hex digit.
Convert each hex digit to its 4-bit nibble. Join them.
Multiply each digit by its place value (16¹, 16⁰) and add.
Divide by 16. Quotient FIRST, remainder SECOND.
If Cambridge ask for hex, give hex. Converting to binary when hex was asked is a recurring mark loss.
Cited: 2024 examiner report — "many candidates converted the denary numbers into binary rather than hexadecimal"What is a key benefit of hexadecimal over binary?
Convert the hex value shown to the requested format. Randomises across all 4 directions.
Press Start.
Stretch: 5 in a row without a mistake across all 4 directions.
Which statement contains a mistake that examiners have flagged?
Press New Question.
Stretch: after you get it right, explain out loud why the wrong statement is wrong using the exam-answer phrasing.
HTML colours use hex codes like #FF5733. Each pair of hex digits controls Red, Green, or Blue (0–255 denary).
What denary value does the channel FF represent?
Stretch: can you predict the swatch colour before submitting?
Type the missing values. Aim for 3 in a row without error.
Press New Question.
Stretch: recite A=10, B=11, C=12, D=13, E=14, F=15 without pausing.
Answer as many hex-related questions as you can in 60 seconds. Warm-up before Practice or Exam.
Press Start Sprint to begin.
Stretch: beat your personal best twice in a session.
Weak skills come round twice as often; strong ones five times less. No question repeats immediately. 20 questions across 9 skills.
Press New Question.
12 questions in Cambridge Paper 1 style. Every question cites its source. Write your answer, then click Mark for keyword-based scoring.
Press New Question to begin.
Press New Question.
Every trap below is drawn from a real Cambridge examiner report or a recurring pattern flagged across multiple sessions.
The computer still stores everything in binary. Hex is a human-readable shorthand only.
Cited: 2024 Mar examiner reportQuotient FIRST, remainder SECOND. 236 = 14 rem 12 → EC, not CE.
Cited: 2024 M/J examiner report — "some candidates gave the correct values but in the incorrect order, that is, CE instead of EC"Read the question wording. If it asks for hex, the answer must be hex.
Cited: 2024 examiner report — "many candidates converted the denary numbers into binary rather than hexadecimal"Each nibble maxes at F. 12 bits = 3 nibbles = 3 hex digits = FFF max.
Cited: 2025 examiner focus on bit-count questionsNever say hex is faster for the computer or uses fewer gates. The mark-scheme phrasing is "easier for humans to read / less error-prone / easier to debug".
Cited: 2024 Nov examiner report"Differences" questions require you to describe both binary and hex. "Hex uses A–F" alone is half an answer.
Cited: 2024 Nov examiner reportIf a nibble converts to 0, you must still write "0". Don't skip it. 00001101 = 0D, not just D.
If asked "how many bits are needed" for a hex number, count nibbles × 4. Don't accidentally give the binary conversion instead.
Cited: 2023 examiner report — "Some candidates incorrectly gave the binary number for the hexadecimal number, rather than the number of bits needed"Common fill-blank slip. Hex has 16 symbols so base = 16. If asked for hex base, it's not 10.
Cited: 2024 examiner reportHex digits after 9: A=10, B=11, C=12, D=13, E=14, F=15. Just continue the alphabet for 6 more values.
4 bits → 1 hex digit. 8 bits → 2 hex digits. 12 bits → 3 hex digits. The pattern: divide bit-count by 4.
When dividing by 16: the whole-number answer goes on the LEFT, the remainder goes on the RIGHT. Think "Question before Rest."
When asked why hex is used, always start "It's easier for humans to…". The computer doesn't care — it uses binary either way.
Circle the target format in the question before you start converting. "hex", "binary", "denary", "bits" — get the right one before you begin.
A zero-value nibble must be written. Don't drop it. 00001101 becomes 0D, not D.
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