Real-world rules become logic. Read the problem statement, check what each 0 and 1 means, then write the expression, choose the circuit and complete the truth table.
The Gates Lab taught you the six gates. The Composition Lab taught you to move between expressions, circuits and truth tables. In this lab you start from a problem statement — a real situation described in words. A typical question gives you:
Your job: write the logic expression, draw the circuit and complete the truth table. All three must match the statement — and each other.
"The circuit solves a real problem." Gates were the building blocks; circuits combined them. Now you use circuits to describe how something in the real world should behave.
Before you write anything, read the input table. For each input, note which value (0 or 1) matches the wording in the statement.
Why first? The statement is written in everyday words, and those words don't always match the 1 value. If the table says "T = 0: temperature 50°C or above" and the statement says "the temperature is 50°C or above", you need NOT T.
Take each condition in the statement, look up its input in the table, and write it as an input or NOT input:
A = 1 operator present · write: AB = 1 key not present · write: B (the table already says "not present" — no NOT needed)C = 1 code not correct · write: NOT C (opposite — invert)| Words in the statement | Gate |
|---|---|
| "and", "both … and …", "all of" | AND |
| "or", "either … or …" | OR |
| "either … or …, but not both", "exactly one of" | XOR |
| "unless X", "but not if X" | AND NOT X |
| "only if X" | X AND (X must be true for the output to be 1) |
Put brackets around each group: "A and either B or C" is A AND (B OR C), not A AND B OR C.
Once you have the expression, draw the circuit and fill the truth table from that expression. Then test one or two rows against the statement in words: "the operator is present and the key is present — does the crane move?" If a row doesn't make sense, re-read the input table.
Write the expression and draw the circuit for the statement as it is worded — one gate for each condition and joining word. Don't rewrite or simplify it.
Some of these are noted in Cambridge examiner reports; the rest come from the syllabus and good exam habits. Every one has a fix.
Typical instructions in problem-statement questions, and what they ask you to do.
0 / 6 revealed
T or NOT T?NOT T. The "hot" condition is the 0 value, so you invert it to get 1 when it's hot.AND NOT R — the output can only be 1 when the reset is not active.The Gates Lab taught you the gates, the Composition Lab taught you to combine them, and this lab taught you to use them on real problems.
Next up: Topic 11 Programming Scenarios.
10.1–10.7 Gates Lab
10.8–10.10 Composition Lab
📍 10.11 Problem Statements Lab (this page)
Next: Topic 11 Programming Scenarios
Covers Cambridge 0478 Topic 10, outcome 3: (a) create a logic circuit, (b) complete a truth table and (c) write a logic expression — each from a problem statement. Circuits have up to three inputs and one output, and are drawn as given, without simplification.
Learn slows down what Book Notes covered, using one scenario all the way through. Then head to Activities for 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 input table. B and C are the opposite way round to the statement: B = 1 means the key is not present, and C = 1 means the code is not correct.
Step 2 · Turn each condition into a small expression.
ANOT BNOT CStep 3 · Join them. "and either … or …" → AND ( … OR … ):
The markers on this page accept the parts in any order, and with or without X =. A rewritten version that only behaves the same — such as A AND NOT (B AND C) — gets a tip instead of the marks, because it isn't the circuit the statement describes.
Questions sometimes give an input the opposite way round to the wording in the statement. Skipping the input table loses marks.
"ignition key is present" → looks like B
X = A AND (B OR C)
❌ The crane moves when the key is missing
B = 0 when the key is present → NOT B
X = A AND (NOT B OR NOT C)
✅ Matches the statement
Habit: read the input table before you write anything. Every time.
Most statements use and and or. Watch for these too:
U XOR DAND NOT RP AND …A.B, OR as A + B and NOT as a bar over the letter. In this course write logic expressions in words, using the gate names.The Activities tab has 4 modes: Statement → Expression · Statement → Truth table · Statement → Circuit · Full problem. The Full problem mode unlocks once you've checked an answer in each of the first three.
This lab covers Topic 10, outcome 3, starting from a problem statement:
Four modes, each a different part of a problem-statement question. Each answer is checked against the statement: expressions must describe the same circuit (parts in any order are fine), truth tables are checked row by row.
Unlocking: Mode 4 (Full problem) unlocks once you've checked an answer in each of Modes 1, 2 and 3.
Quick questions: read a statement and its input table, then work out the output for one row. Streaks show at 3 · 6 · 10 correct. Sprint is for speed — it doesn't change your Mastery.
12 scenarios in the style of Paper 2 questions. Tap one to try it. ✅ = answered correctly in any mode.
Mode 1 · Write the logic expression for the statement.
Mode 2 · Complete the truth table, with the inputs in the order given.
Mode 3 · Choose the circuit that matches the statement, from three. Sketch it on paper first.
Mode 4 · All three parts for one statement, each marked separately — like a full exam question.
Skills you get wrong come back more often. Filter by difficulty or run the whole pool. Missed questions are saved to Mistakes.
Paper 2 style problem-statement questions. Answer every part, then press Mark my answer — expressions, circuits and truth tables are checked automatically.
Written in the style of Cambridge Paper 2. The scenarios are made up for practice. In the real exam you draw the circuit — sketch it on paper first, then use the "choose the circuit" parts to check your drawing.
Read these before your exam. Then look at Mistakes to see the ones you make.
Six one-liners to recite before your exam.
Tick each item as you master it. In the skill grid, tap a status chip to set it yourself. When all 12 are ticked, the Module Mastered banner unlocks.
Mastered = 3+ attempts and ≥70% accuracy. Tap the status chip to override it.
That's the end of Topic 10: Boolean Logic. Next, Topic 11 practises the longer programming scenario question.
10.1–10.7 Gates Lab
10.8–10.10 Composition Lab
📍 10.11 Problem Statements Lab (this page)
Next: Topic 11 Programming Scenarios
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