10. Boolean Logic
Logic gates (NOT, AND, OR, NAND, NOR, XOR), logic circuits, truth tables and logic expressions.
In the 2029–31 syllabus logic moves to Paper 1: gates in 1.1 and circuits, truth tables and expressions in 2.1. What changes in 2029 → · Study the new topics: 1. Data representation and logic gates, 2. Logic circuits and hardware
Statometer63CoreNext Paper 294%Everything for this topic — study hub
O Level / IGCSE · 2210 · 0478 · Paper 2
This topic is rows 36–39 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
Core · #10 of 10 in O Level / IGCSE · recomputed with every new session
A regular, well-paid topic — you cannot afford a gap here.
- Next Paper 2
- 94%
- 9 in 10 chance it is set
- Marks a paper
- 8.9 / 75
- 12% of Paper 2 · fair share 25%
- Appeared in
- 25 / 25
- Paper 2 sittings 2023–2026
- Last set
- May/Jun 2026
- 0478/23 · Q7 · 8 marks · 11-series streak
What the papers say
- Set in 25 of 25 Paper 2 sittings on the current syllabus — treat it as certain.
- Worth about 8.9 marks a paper (12% of Paper 2, well under its fair share of 25%).
- Last set May/Jun 2026 · 0478/23 · Q7 for 8 marks — in the most recent series.
- Set in each of the last 11 series without a miss.
- Steady at around 9 marks a paper year on year.
- Lives on “Complete” and “Draw” — 97% of its questions: you must produce something — code, a diagram, a table — practise doing it, not reading it.
- 100% of its questions involve a diagram, table or figure — practise with pen and paper.
- 84% of its questions are set out as code, pseudocode or a table to complete.
- Most of its marks (96%) come in extended questions of 6+ marks — plan the answer before writing.
- Its biggest question so far: 14 marks (Oct/Nov 2025 · 0478/21 · Q4).
- Inside the topic, Truth tables from a problem statement, logic expression or logic circuit carries the most marks (32%) and Logic circuits from a problem statement, logic expression or truth table the least (20%).
- It is examined almost entirely as AO2 (Apply to a context, 93%) — you must apply it to the scenario or the given data — a definition alone will not score.
- The examiner has commented on 59 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 mk0
- 3–4 mk7
- 5–6 mk4
- 7–9 mk50
- 10+ mk31
Average 8.7 marks a question · 100% with a figure or table · 84% with code · biggest 14 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 2 as a whole
| Paper 2 | Syllabus | Measured |
|---|---|---|
| AO1 Knowledge & understanding | 20% | 27% |
| AO2 Apply to a context | 60% | 51% |
| AO3 Evaluate & judge | 20% | 22% |
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 2 sitting, exactly like the topic's. Open a bullet for its own Statometer.
Standard symbols and functions of the NOT, AND, OR, NAND, NOR and XOR gates (NOT has one input; the others have two)#19 of 19 on Paper 2Occasional · 2232% next paper1 marks8/25 sittings↘ Oct/Nov 2025Occasional · 2232%
1 · 20% of topic8/25Oct/Nov 20252 series ago · ↘Rotated in occasionally — the bullet students skip and then meet.
- Next Paper 2
- 32%
- 1 in 4
- Marks a paper
- 1
- 1% of the paper · 20% of the topic
- Asked in
- 8 / 25
- Paper 2 sittings · 46 questions
- Last asked
- Oct/Nov 2025
- 0478/21 · Q4 · 2 marks · 2 series ago
- Asked in 8 of 25 Paper 2 sittings — roughly one paper in 3.
- About 1 marks a paper (1% of Paper 2; 20% of the topic's marks across its 4 bullets).
- Last asked Oct/Nov 2025 · 0478/21 · Q4 (2 marks), 2 seriess ago.
- Easing: 1.8 → 0.5 marks a paper.
- Usually “Draw” or “Complete”: you must produce something — code, a diagram, a table — practise doing it, not reading it.
- Biggest chunk of marks so far: 8.5 in Oct/Nov 2023 · 2210/23 · Q6.
- It is examined mostly as AO1 (Knowledge & understanding, 53%), the rest AO2 (48%) — definitions and descriptions in syllabus words score.
Last 12 sittings↘ EasingAssessment objectives
AO1 53%AO2 48%- AO1 Knowledge & understanding
- AO2 Apply to a context
- AO3 Evaluate & judge
- Draw74%
- Complete67%
- Consider39%
- State15%
Logic circuits from a problem statement, logic expression or truth table#15 of 19 on Paper 2Regular · 3559% next paper1.3 marks15/25 sittings→ May/Jun 2026Regular · 3559%
1.3 · 20% of topic15/25May/Jun 2026latest series · →Set most sessions for a few marks; know the definition and one example.Syllabus: drawn as stated, up to three inputs and one output
- Next Paper 2
- 59%
- 6 in 10
- Marks a paper
- 1.3
- 2% of the paper · 20% of the topic
- Asked in
- 15 / 25
- Paper 2 sittings · 54 questions
- Last asked
- May/Jun 2026
- 0478/23 · Q7 · 2 marks · 11-series streak
- Asked in 15 of 25 Paper 2 sittings — about 6 papers in 10.
- About 1.3 marks a paper (2% of Paper 2; 20% of the topic's marks across its 4 bullets).
- Last asked May/Jun 2026 · 0478/23 · Q7 (2 marks) — in the most recent series.
- Asked in each of the last 11 series.
- Usually “Draw” or “Complete”: you must produce something — code, a diagram, a table — practise doing it, not reading it.
- It is examined almost entirely as AO2 (Apply to a context, 100%) — you must apply it to the scenario or the given data — a definition alone will not score.
Last 12 sittings→ SteadyAssessment objectives
AO2 100%- AO1 Knowledge & understanding
- AO2 Apply to a context
- AO3 Evaluate & judge
- Draw91%
- Complete87%
- Consider46%
- Write11%
Truth tables from a problem statement, logic expression or logic circuit#11 of 19 on Paper 2Core · 5887% next paper2.6 marks23/25 sittings→ May/Jun 2026Core · 5887%
2.6 · 32% of topic23/25May/Jun 2026latest series · →A regular earner inside the topic — most papers touch it.
- Next Paper 2
- 87%
- 9 in 10
- Marks a paper
- 2.6
- 4% of the paper · 32% of the topic
- Asked in
- 23 / 25
- Paper 2 sittings · 77 questions
- Last asked
- May/Jun 2026
- 0478/23 · Q7 · 2 marks · 11-series streak
- Asked in 23 of 25 Paper 2 sittings — nearly every paper.
- About 2.6 marks a paper (4% of Paper 2; 32% of the topic's marks across its 4 bullets).
- Last asked May/Jun 2026 · 0478/23 · Q7 (2 marks) — in the most recent series.
- Asked in each of the last 11 series.
- Usually “Complete” or “Draw”: you must produce something — code, a diagram, a table — practise doing it, not reading it.
- Biggest chunk of marks so far: 4 in May/Jun 2026 · 2210/21 · Q8.
- It is examined almost entirely as AO2 (Apply to a context, 100%) — you must apply it to the scenario or the given data — a definition alone will not score.
Last 12 sittings→ SteadyAssessment objectives
AO2 100%- AO1 Knowledge & understanding
- AO2 Apply to a context
- AO3 Evaluate & judge
- Complete96%
- Draw69%
- Consider53%
- Write21%
Logic expressions from a problem statement, logic circuit or truth table#8 of 19 on Paper 2Core · 6286% next paper3.1 marks22/25 sittings→ May/Jun 2026Core · 6286%
3.1 · 28% of topic22/25May/Jun 2026latest series · →A regular earner inside the topic — most papers touch it.
- Next Paper 2
- 86%
- 9 in 10
- Marks a paper
- 3.1
- 4% of the paper · 28% of the topic
- Asked in
- 22 / 25
- Paper 2 sittings · 59 questions
- Last asked
- May/Jun 2026
- 0478/23 · Q7 · 4 marks · 11-series streak
- Asked in 22 of 25 Paper 2 sittings — nearly every paper.
- About 3.1 marks a paper (4% of Paper 2; 28% of the topic's marks across its 4 bullets).
- Last asked May/Jun 2026 · 0478/23 · Q7 (4 marks) — in the most recent series.
- Asked in each of the last 11 series.
- Usually “Complete” or “Draw”: you must produce something — code, a diagram, a table — practise doing it, not reading it.
- Biggest chunk of marks so far: 4.5 in May/Jun 2026 · 2210/22 · Q8.
- It is examined almost entirely as AO2 (Apply to a context, 100%) — you must apply it to the scenario or the given data — a definition alone will not score.
Last 12 sittings→ SteadyAssessment objectives
AO2 100%- AO1 Knowledge & understanding
- AO2 Apply to a context
- AO3 Evaluate & judge
- Complete92%
- Draw80%
- Consider64%
- Write27%
4% 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, 64 questions) — history, not counted in the rates.
By exam series
- Feb/Mar4/4 · 8.5 mk
- May/Jun12/12 · 8.3 mk
- Oct/Nov9/9 · 9.6 mk
What you need to know4syllabus section 10
- Standard symbols and functions of the NOT, AND, OR, NAND, NOR and XOR gates (NOT has one input; the others have two)
- Logic circuits from a problem statement, logic expression or truth table — drawn as stated, up to three inputs and one output
- Truth tables from a problem statement, logic expression or logic circuit
- Logic expressions from a problem statement, logic circuit or truth table
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Infographics2draw these the way the examiner expects · download as PNG
Logic gate symbols
From logic circuit to truth table
Key terms9use these exact words in the exam
Dotted terms are defined in the glossary.
Code help2referenced to the Cambridge pseudocode guide
DECLARE A, B, C, X : BOOLEANDECLARE i : INTEGERFOR i ← 0 TO 7A ← (i DIV 4) MOD 2 = 1B ← (i DIV 2) MOD 2 = 1C ← i MOD 2 = 1X ← (A AND B) OR NOT COUTPUT A, " ", B, " ", C, " -> ", XNEXT i
💡 This prints the full truth table — compare with the Logic Gates Lab.
// A security light (X) comes on when it is dark (D) AND there is movement (M),// OR when the manual switch (S) is on. X = (D AND M) OR SDECLARE D, M, S : INTEGERDECLARE X : BOOLEANDECLARE Row : STRINGOUTPUT "D M S | X"FOR D ← 0 TO 1FOR M ← 0 TO 1FOR S ← 0 TO 1X ← (D = 1 AND M = 1) OR S = 1IF X THENRow ← "1"ELSERow ← "0"ENDIFOUTPUT D, " ", M, " ", S, " | ", RowNEXT SNEXT MNEXT D
💡 Three inputs → 2³ = 8 rows, listed in binary order 000 to 111 — exactly how an exam truth table is laid out.
Playground examples1runnable program for this topic
- Run
Truth table for a logic expression
Generate all 8 input combinations of A, B, C from a counter and evaluate X = (A AND B) OR NOT C.
Boolean Algebra & K-map Lab3real Paper 3 questions — K-maps, De Morgan's laws, adders, flip-flops — solved and practised
- Open
XOR as a sum-of-products
A ⊕ B = A.B̅ + A̅.B — the half adder's sum output written in Boolean algebra.
- Open
Circuit with working columns P, Q, R, S
June 2024 Q6(a): P = A̅, Q = B.C, R = P NAND Q... build the working columns in gate order, then Z. One mark for the working, one per half of Z.
- Open
Four working columns and an XOR
Nov 2025 Q6(a) style: an XOR, a NAND and an OR feeding a final AND — eight rows, four working columns.
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.
