Real-world problems become gates. Read the scenario. Extract the binary meaning. Produce expression, circuit, and truth table. The syllabus finally asks a real question.
Labs A and B taught you the tools. Lab C is where you use them on real questions. A Cambridge Paper 2 problem-statement question gives you:
Your job: produce an expression, a circuit, and a truth table. All three must agree with each other and with the scenario. That's what the multi-modal marker in Problem Detective drills.
"The composition solves a real problem." Gates were the atoms (Lab A). Composition wired them into functions (Lab B). Purpose applies those functions to the world.
Before you read the scenario carefully, read the mapping table. It tells you what each variable's 0 and 1 mean. Only then read the alarm-condition lines.
Why first? Because the scenario is written in natural language, and natural language rarely lines up with the binary value. Reading the mapping first primes you to catch "opposite" cases (like "the temperature is 50°C or above" mapping to T = 0, needing NOT T in the expression).
Cambridge scenarios list criteria explicitly: "the alarm sounds if condition-1 OR condition-2 AND condition-3…". Take each phrase, look up its variable in the mapping table, and write the partial expression:
A = 1 when operator present · Partial: AB = 1 when key not present · Partial: B (same word — no NOT needed)C = 1 when code NOT correct · Partial: NOT C (opposite — invert)Read the mapping every time. The scenario writer chose which direction to map; you don't get to guess.
Cambridge scenarios use the words AND, OR, and occasionally only if, either, both. Translate:
Bracket generously. Cambridge marks against wrong grouping.
Once you've written the expression, generate the truth table and check the circuit. If any two of the three disagree, one of them is wrong — usually the one with the most complex structure. Trace back to the alarm-condition line and re-read the mapping.
Problem Detective's Mode 4 (Full Challenge) drills this: it shows the 3×3 consistency matrix between your expression, circuit, and truth table. You won't have this tool in the exam — the point is to internalise the cross-check as a habit.
0 / 6 revealed
T or NOT T?NOT T. The mapping puts the "hot" condition on the 0 side, so you need to invert to get 1 when hot. Read the mapping every time.Signal (Lab A) taught you the gates. Circuit (Lab B) taught you to compose them. Purpose (this lab) taught you to apply that composition to real problems.
Next up: Topic 11 or an exam-focused revision cycle across all three labs. The interactive-heavy work of Topic 10 is done — you own the syllabus material.
This is the third and final lab of Topic 10. Signal → Circuit → Purpose. The syllabus finally asks a real question, and you can answer it in all three forms.
The composition solves a real problem.
Learn slows down what Book Notes covered. Try the 3-step method on a scenario preview, then head to Activities for the full Problem Detective.
| Input | Binary value | Description |
|---|---|---|
| A | 0 | operator not present |
| 1 | operator present | |
| B | 0 | ignition key present |
| 1 | ignition key not present | |
| C | 0 | operator code correct |
| 1 | operator code not correct |
Step 1 · Read the mapping table. Notice B and C are opposite to the natural reading — B = 1 means the key is not present, C = 1 means the code is not correct.
Step 2 · Extract each condition.
ANOT BNOT CStep 3 · Combine with the scenario's connectives. "and either X or Y" → AND (X OR Y). Full expression:
Note: the Cambridge mark scheme accepts multiple equivalent forms. The parser will accept any behaviourally-equivalent expression — commutative rearrangements and De Morgan-legal transforms all pass.
Cambridge deliberately writes some mappings opposite to the natural reading. Students who skip the mapping table lose easy marks.
"ignition key is present" → looks like B = 1
Expression: A AND (B OR C)
❌ Loses marks — didn't read the mapping
Mapping: B = 0 when key present → invert
Expression: A AND (NOT B OR NOT C)
✅ Full marks — mapping table respected
Habit: read the mapping table before the scenario. Every time. Cambridge writes opposite mappings on purpose.
The Activities tab has 5 modes: Statement → Expression · Statement → Truth Table · Statement → Circuit · Full Challenge (Guided · sequential) · Full Challenge (Free · parallel). Modes 4b (Free) unlocks after you complete 3 different scenarios in 4a (Guided).
2023+ Paper 2 questions: crane (2025 P22 Q8), security (2025 P23 Q7), safe (2024 P22 Q8), window (2024 P23 Q8).
Five modes. Each teaches one facet of the composition-solves-a-real-problem skill. The multi-modal marker checks your expression, circuit, and truth table for consistency with each other and with the reference — mirroring how Cambridge marks each representation separately.
Progressive disclosure: Mode 4b (Full Challenge · Free) unlocks after you complete 3 different scenarios in Mode 4a (Full Challenge · Guided).
⌨️ Keyboard: Tab through mode buttons · Arrow keys within mode selector · Enter to activate · Tab into textarea / TT cells · Arrow keys navigate cells · 0/1 to fill · Space on gate palette to pick up gates.
Mixed prompts from Mode 1 (expression) and Mode 2 (truth-table row prediction). Mode 4b excluded — too multi-panel for a 60s timer. Weak scenarios surface 2× more often.
12 scenarios · 4 from real Paper 2, 2 from textbook, 6 synthetic (following the Paper 2 pattern)
Mode 1 · Write the expression only. Fast reps.
Mode 2 · Fill the truth table only. Cell-by-cell.
Mode 3 · Write an expression that the circuit renderer will draw for you (so you see the circuit form of your answer).
Mode 4a · Sequential 3-step Full Challenge · Step 2 locked until Step 1 green.
Mode 4b · Parallel Full Challenge · all three surfaces at once + 3×3 consistency matrix. Unlocks after 3 completed 4a scenarios.
Distributed across the 5 Problem Detective modes and the 10 traps. Adaptive: weak modes surface 2× more often.
Real Cambridge Paper 2 (P22/P23) problem-statement questions from 2024 and 2025, plus composite exam-style. Write your answer, then self-mark against the mark scheme.
Read before your exam. The examiner-cited traps are the ones the 2025 P22 report flagged.
Six one-liners. Recite these before your exam.
Tick each item as you master it. All 12 ticked → Module Mastered banner.
Mastered = 3+ attempts and ≥70% accuracy. Tap to override.
Every wrong answer captures here automatically.
Your attempts, accuracy, and mastery counts across Lab C.