1. Data Representation
Everything is numbers. Learn how binary, hexadecimal, text, images and sound are stored and how data is compressed.
In the 2029–31 syllabus this becomes Topic 1 (with logic gates). File-size calculations and PiB/EiB go; cyclic shifts, Huffman coding and the command word Convert arrive. What changes in 2029 → · Study the new topic: 1. Data representation and logic gates
Statometer94BankerNext Paper 194%Everything for this topic — study hub
O Level / IGCSE · 2210 · 0478 · Paper 1
This topic is rows 1–4 of the study route.Open it on your study route
Statometer — what 25 real papers say about this topic and each of its 4 syllabus bullets
Banker · #3 of 10 in O Level / IGCSE · recomputed with every new session
Set in nearly every paper and worth a big slice of it — revise first, expect it.
- Next Paper 1
- 94%
- 9 in 10 chance it is set
- Marks a paper
- 20.7 / 75
- 28% of Paper 1 · fair share 17%
- Appeared in
- 25 / 25
- Paper 1 sittings 2023–2026
- Last set
- May/Jun 2026
- 0478/13 · Q8 · 10 marks · 11-series streak
What the papers say
- Set in 25 of 25 Paper 1 sittings on the current syllabus — treat it as certain.
- Worth about 20.7 marks a paper (28% of Paper 1, 1.7× its fair share).
- Last set May/Jun 2026 · 0478/13 · Q8 for 10 marks — in the most recent series.
- Set in each of the last 11 series without a miss.
- Rising: about 19.1 marks a paper in the earlier years, 21.8 in the latest.
- Lives on “Give” and “Explain” — 66% of its questions: short, precise answers in syllabus words.
- Most of its marks (88%) come in extended questions of 6+ marks — plan the answer before writing.
- Its biggest question so far: 24 marks (Oct/Nov 2024 · 2210/13 · Q2).
- Inside the topic, §1.1 Number systems carries the most marks (53%) and §1.1 Binary arithmetic the least (7%).
- It is examined as a mix: AO1 46%, AO2 41% — definitions and descriptions in syllabus words score.
- The examiner has commented on 111 of its questions — read “What the examiner said” before you practise.
Command words
Share of questions using the word (a question can use several). What each wants →
Question shapes
- 1–2 mk5
- 3–4 mk22
- 5–6 mk38
- 7–9 mk39
- 10+ mk56
Average 8.6 marks a question · 16% with a figure or table · 34% with code · biggest 24 marks
Assessment objectives — how it is examined
Every part of every current-syllabus question filed under Cambridge's AO1 / AO2 / AO3 (from its command word and what it asks you to do), so you know whether this topic pays for definitions, for applying, or for judging and building.
- AO1 Knowledge & understanding
- AO2 Apply to a context
- AO3 Evaluate & judge
Paper 1 as a whole
| Paper 1 | Syllabus | Measured |
|---|---|---|
| AO1 Knowledge & understanding | 60% | 64% |
| AO2 Apply to a context | 20% | 24% |
| AO3 Evaluate & judge | 20% | 12% |
Syllabus = Cambridge's grid; measured = the bank's current-syllabus papers.
Inside the topic — every syllabus bullet, measured
Each part of each question is filed under the bullet it examines; the numbers are per Paper 1 sitting, exactly like the topic's. Open a bullet for its own Statometer.
1.1Number systems#1 of 20 on Paper 1Banker · 9694% next paper7.1 marks25/25 sittings→ May/Jun 2026Banker · 9694%
7.1 · 53% of topic25/25May/Jun 2026latest series · →Asked in nearly every paper — the bullet to know cold.Syllabus: why computers use binary; denary, binary and hexadecimal; converting between them (up to 16 bits); where hexadecimal is used and why
- Next Paper 1
- 94%
- 9 in 10
- Marks a paper
- 7.1
- 10% of the paper · 53% of the topic
- Asked in
- 25 / 25
- Paper 1 sittings · 90 questions
- Last asked
- May/Jun 2026
- 0478/13 · Q8 · 10 marks · 11-series streak
- Asked in 25 of 25 Paper 1 sittings — nearly every paper.
- About 7.1 marks a paper (10% of Paper 1; 53% of the topic's marks across its 4 bullets).
- Last asked May/Jun 2026 · 0478/13 · Q8 (10 marks) — in the most recent series.
- Asked in each of the last 11 series.
- Usually “Give” or “Convert”: short, precise answers in syllabus words.
- Biggest chunk of marks so far: 11 in Oct/Nov 2025 · 2210/13 · Q1.
- It is examined mostly as AO2 (Apply to a context, 64%), the rest AO1 (30%) — you must apply it to the scenario or the given data — a definition alone will not score.
Last 12 sittings→ SteadyAssessment objectives
AO1 30%AO2 64%- AO1 Knowledge & understanding
- AO2 Apply to a context
- AO3 Evaluate & judge
- Give56%
- Convert44%
- Show34%
- Explain32%
1.1Binary arithmetic#14 of 20 on Paper 1Core · 5680% next paper2.6 marks21/25 sittings→ May/Jun 2026Core · 5680%
2.6 · 7% of topic21/25May/Jun 2026latest series · →A regular earner inside the topic — most papers touch it.Syllabus: adding two 8-bit integers; overflow; logical left and right shifts; two's complement for positive and negative 8-bit integers
- Next Paper 1
- 80%
- 8 in 10
- Marks a paper
- 2.6
- 4% of the paper · 7% of the topic
- Asked in
- 21 / 25
- Paper 1 sittings · 26 questions
- Last asked
- May/Jun 2026
- 2210/12 · Q1 · 2.5 marks · 10-series streak
- Asked in 21 of 25 Paper 1 sittings — about 8 papers in 10.
- About 2.6 marks a paper (4% of Paper 1; 7% of the topic's marks across its 4 bullets).
- Last asked May/Jun 2026 · 2210/12 · Q1 (2.5 marks) — in the most recent series.
- Asked in each of the last 10 series.
- Usually “Give” or “Show”: short, precise answers in syllabus words.
- Biggest chunk of marks so far: 6 in Oct/Nov 2023 · 2210/12 · Q2.
- It is examined almost entirely as AO2 (Apply to a context, 77%) — you must apply it to the scenario or the given data — a definition alone will not score.
Last 12 sittings→ SteadyAssessment objectives
AO1 17%AO2 77%- AO1 Knowledge & understanding
- AO2 Apply to a context
- AO3 Evaluate & judge
- Give89%
- Show73%
- Convert50%
- State35%
1.2Text, sound and images#12 of 20 on Paper 1Core · 5873% next paper3.1 marks19/25 sittings→ May/Jun 2026Core · 5873%
3.1 · 12% of topic19/25May/Jun 2026latest series · →A regular earner inside the topic — most papers touch it.Syllabus: character sets (ASCII, Unicode); sample rate and sample resolution; pixels, image resolution and colour depth; effects on file size and quality
- Next Paper 1
- 73%
- 7 in 10
- Marks a paper
- 3.1
- 4% of the paper · 12% of the topic
- Asked in
- 19 / 25
- Paper 1 sittings · 34 questions
- Last asked
- May/Jun 2026
- 0478/13 · Q1 · 3 marks
- Asked in 19 of 25 Paper 1 sittings — about 8 papers in 10.
- About 3.1 marks a paper (4% of Paper 1; 12% of the topic's marks across its 4 bullets).
- Last asked May/Jun 2026 · 0478/13 · Q1 (3 marks) — in the most recent series.
- Usually “Give” or “Explain”: short, precise answers in syllabus words.
- Biggest chunk of marks so far: 11 in Oct/Nov 2023 · 0478/11 · Q5.
- It is examined mostly as AO1 (Knowledge & understanding, 60%), the rest AO2 (30%) — definitions and descriptions in syllabus words score.
Last 12 sittings→ SteadyAssessment objectives
AO1 60%AO2 30%- AO1 Knowledge & understanding
- AO2 Apply to a context
- AO3 Evaluate & judge
- Give62%
- Explain38%
- State38%
- Identify27%
1.3Data storage and compression#8 of 20 on Paper 1Core · 6581% next paper3.7 marks21/25 sittings↗ May/Jun 2026Core · 6581%
3.7 · 27% of topic21/25May/Jun 2026latest series · ↗A regular earner inside the topic — most papers touch it.Syllabus: bit, nibble, byte, KiB … EiB (1024-based); calculating image and sound file sizes; why compress; lossy vs lossless (run-length encoding)
- Next Paper 1
- 81%
- 8 in 10
- Marks a paper
- 3.7
- 5% of the paper · 27% of the topic
- Asked in
- 21 / 25
- Paper 1 sittings · 75 questions
- Last asked
- May/Jun 2026
- 0478/13 · Q1 · 4 marks · 7-series streak
- Asked in 21 of 25 Paper 1 sittings — about 8 papers in 10.
- About 3.7 marks a paper (5% of Paper 1; 27% of the topic's marks across its 4 bullets).
- Last asked May/Jun 2026 · 0478/13 · Q1 (4 marks) — in the most recent series.
- Asked in each of the last 7 series.
- Rising: 3.4 → 4 marks a paper.
- Usually “Give” or “State”: short, precise answers in syllabus words.
- Biggest chunk of marks so far: 8 in Feb/Mar 2025 · 0478/12 · Q2.
- It is examined mostly as AO1 (Knowledge & understanding, 55%), the rest AO3 (33%) — definitions and descriptions in syllabus words score.
Last 12 sittings↗ RisingAssessment objectives
AO1 55%AO3 33%- AO1 Knowledge & understanding
- AO2 Apply to a context
- AO3 Evaluate & judge
- Give48%
- State41%
- Explain39%
- Describe25%
27% of the topic's marks sit in question parts that belong to another topic (scenario questions cross sections) or that no bullet claims; they count for the topic, not for a bullet.
Marks a paper, year by year
Grey years are the previous syllabus (2011–2022, 108 questions) — history, not counted in the rates.
By exam series
- Feb/Mar4/4 · 17.8 mk
- May/Jun12/12 · 19.1 mk
- Oct/Nov9/9 · 22.6 mk
What you need to know4syllabus §1.1, §1.2, §1.3
- 1.1Number systems — why computers use binary; denary, binary and hexadecimal; converting between them (up to 16 bits); where hexadecimal is used and why
- 1.1Binary arithmetic — adding two 8-bit integers; overflow; logical left and right shifts; two's complement for positive and negative 8-bit integers
- 1.2Text, sound and images — character sets (ASCII, Unicode); sample rate and sample resolution; pixels, image resolution and colour depth; effects on file size and quality
- 1.3Data storage and compression — bit, nibble, byte, KiB … EiB (1024-based); calculating image and sound file sizes; why compress; lossy vs lossless (run-length encoding)
Video lectures44ZAK's YouTube channel · play here
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Infographics5draw these the way the examiner expects · download as PNG
Number system conversions
File size calculations
Two's complement, overflow & shifts
Bitmap, vector & sound
Lossless vs lossy compression
Key terms10use these exact words in the exam
Dotted terms are defined in the glossary.
Code help3referenced to the Cambridge pseudocode guide
DECLARE N, Bit : INTEGERDECLARE Binary : STRINGN ← 182Binary ← ""REPEATBit ← N MOD 2Binary ← NUM_TO_STR(Bit) & Binary // remainders read bottom-upN ← N DIV 2UNTIL N = 0OUTPUT Binary
💡 Exactly the method the mark scheme wants: divide by 2, collect remainders in reverse.
DECLARE B : STRINGDECLARE i, Total, Place : INTEGERB ← "10110110"Total ← 0Place ← 1FOR i ← LENGTH(B) TO 1 STEP -1IF SUBSTRING(B, i, 1) = "1" THENTotal ← Total + PlaceENDIFPlace ← Place * 2NEXT iOUTPUT Total
DECLARE V : INTEGERV ← 22 // 0001 0110OUTPUT V * 4 // shift left 2 → 88OUTPUT V DIV 2 // shift right 1 → 11
Playground examples7runnable programs for this topic
- Run
Denary → binary by repeated division
MOD 2 gives each bit, DIV 2 moves on; the remainders are read bottom-up.
- Run
Binary → denary with place values
Walk the bits from the right, doubling the place value each time.
- Run
Denary → hexadecimal
Same idea as binary but MOD 16, with a lookup string for the digits A–F.
- Run
Two's complement — negate an 8-bit number
Invert every bit, then add 1 with a carry that ripples from the right.
- Run
Run-length encoding (lossless compression)
Replace runs of the same character with a count and the character.
- Run
Binary, hex and two's complement
bin(), hex(), int(s, 2) and format() — plus two's complement of a negative number by hand.
- Run
Logic gates and a truth table
Build AND, OR, XOR, NAND from Boolean operators and print the truth table of an expression.
Also for this topic: 2 Java programs · 2 VB.NET programs in the browser compilers.
Test yourself
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NewCS Games · 16 to play
Revise this topic by playing
Quiz battles, a daily CS word, SQL whodunnits, logic-gate puzzles and arcade — every game drills the syllabus. Solo against AskZ bots, with friends, or with your whole class. Free, no sign-up.
