Spec & Goals 3 min
AQA Spec 3.4.2 · Boolean logic
By the end of this lesson you can:
- Trace a logic circuit made from combined gates, gate by gate.
- Complete a truth table for a circuit, adding a column per gate.
- Write the Boolean expression that describes a circuit.
Warm-Up 5 min
Last lesson you met the three gates — AND, OR and NOT — and their truth tables.
Quick starter
An AND gate has inputs A=1 and B=0. What is its output?
Reveal the answer
The output is 0. An AND gate outputs 1 only when both inputs are 1.
Key Concept — combining gates 14 min
A single gate is rarely enough. We join gates together so the output of one becomes the input of the next.
Reading a circuit
To find a circuit's output, work through it gate by gate. Start at the inputs on the left and follow the wires to the right.
You solve each gate using the inputs you already know, then carry its output forward as the input to the next gate.
Describing a circuit with Boolean
A circuit can be written as a Boolean expression using AND, OR and NOT.
Brackets show which part is solved first — just like in maths. We build the expression from a problem statement, then wire the gates to match.
Worked Example — a two-gate circuit 12 min
Problem: a security alarm sounds (Q) when both the door A and window B sensors are triggered, or when the manual switch C is not set.
Here is the circuit. An AND gate combines A and B; a NOT gate inverts C; an OR gate combines those two results into Q.
P = A AND B, R = NOT C, and the output Q = P OR R.Build the truth table column by column
Add a column for each gate: P = A AND B, then R = NOT C, then Q = P OR R. Fill it left to right.
| A | B | C | P = A AND B | R = NOT C | Q = P OR R |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 1 |
The Boolean expression for the whole circuit is:
Q = (A AND B) OR (NOT C)
Try It Yourself 12 min
Goal: For the worked circuit, state the output Q when A=0, B=0 and C=0.
Hint: work out P = A AND B and R = NOT C first, then P OR R.
Goal: Write the Boolean expression for a circuit where Q is (A OR B) AND C.
Hint: the brackets show the OR gate is solved before the AND gate.
Goal: Complete a truth table for Q = (NOT A) AND (B OR C). Add a column for each gate.
Hint: three inputs give eight rows; add columns for NOT A, B OR C, then Q.
📝 Exam Practice 10 min
Answer the way the examiner expects — the command word and the marks tell you how much to write.
Complete the truth table for the logic circuit shown in the worked example, Q = (A AND B) OR (NOT C).
| A | B | C | Q |
|---|---|---|---|
| 0 | 0 | 0 | |
| 0 | 1 | 1 | |
| 1 | 1 | 0 |
Mark scheme
- Row A=0, B=0, C=0 → Q = 1 (1).
- Row A=0, B=1, C=1 → Q = 0 (1).
- Row A=1, B=1, C=0 → Q = 1 (1).
Write the Boolean expression for the circuit shown in the worked example.
Mark scheme
A AND BandNOT Cidentified, with brackets (1).- Combined with
OR:Q = (A AND B) OR (NOT C)(1).
State the output Q of the circuit when A=1, B=0 and C=1.
Mark scheme
- 0 (1) — because
A AND B = 0andNOT C = 0, so0 OR 0 = 0.
Which gate's output goes straight to Q in the worked circuit?
A) AND B) NOT C) OR D) NAND
Mark scheme
- C — the OR gate (1).
Recap & Key Terms 3 min
Gates can be combined into a logic circuit. To find the output, work through it gate by gate. A circuit can be written as a Boolean expression and built from a problem statement. In the truth table, add a column for each gate and fill it left to right.
- Logic circuit
- Two or more logic gates combined, where one gate's output feeds the next.
- Boolean expression
- A statement using
AND,ORandNOTthat describes a circuit's output, e.g.Q = (A AND B) OR (NOT C). - Combined gates
- Gates wired together so signals flow through them in order, left to right.
Homework 1 min
Task (≤ 15 min): Draw a labelled truth table for the circuit Q = (A OR B) AND (NOT C). Add a column for each gate and fill in all eight rows.
Model answer
Columns: A, B, C, A OR B, NOT C, Q.
Q = 1 only when (A OR B) = 1 and C = 0: rows (0,1,0), (1,0,0) and (1,1,0).
Award marks for: correct A OR B column (1), correct NOT C column (1), correct Q column (1).