Boolean Logic and Logic Gates — GCSE Computer Science Complete Guide
Boolean logic explained for GCSE Computer Science. AND, OR, NOT, NAND, NOR, XOR truth tables, drawing circuits from expressions, and exam technique for AQA, OCR and Cambridge.
Gareth Edgell
Head of CS · Senior Examiner · 15+ years tutoring
Boolean logic is one of the topics in GCSE Computer Science where students either score full marks or lose marks they should not. The truth tables themselves are not difficult — what catches students out is drawing circuits from expressions, completing truth tables for multi-gate circuits, and forgetting NAND and NOR.
This guide covers everything you need for the exam.
The six gates you need to know
Every GCSE specification covers these six logic gates. You need to know: the symbol (for drawing circuits), the truth table (for completing or verifying), and the rule (for instant answers).
AND gate
Rule: Output is 1 only when BOTH inputs are 1.
| A | B | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Memory aid: AND = “all inputs must be 1”. Only the all-1s row gives 1.
OR gate
Rule: Output is 1 when AT LEAST ONE input is 1.
| A | B | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Memory aid: OR = “at least one”. Only the all-0s row gives 0.
NOT gate (inverter)
Rule: Output is the opposite of the input.
| A | Output |
|---|---|
| 0 | 1 |
| 1 | 0 |
Single input only. Simply flips the value.
NAND gate
Rule: Inverted AND — output is 0 only when BOTH inputs are 1.
| A | B | Output |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Memory aid: NAND = NOT AND. Take the AND output and flip every bit. The only row that gives 0 is the all-1s row.
NOR gate
Rule: Inverted OR — output is 1 only when BOTH inputs are 0.
| A | B | Output |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
Memory aid: NOR = NOT OR. Take the OR output and flip. Only the all-0s row gives 1.
XOR gate (Exclusive OR)
Rule: Output is 1 when inputs are DIFFERENT.
| A | B | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Memory aid: XOR = “eXclusive OR”. Both 1 (identical) gives 0. Both 0 (identical) gives 0. Different gives 1.
Universal gates — NAND and NOR
NAND and NOR are called universal gates because any other logic gate can be built entirely from NAND gates, or entirely from NOR gates. You may be asked to demonstrate this:
NOT from NAND: Connect both inputs of a NAND gate together (both to input A). The output is NOT A.
AND from NAND: Two NAND gates — first NAND A and B, then NAND the result with itself (NOT it). This gives A AND B.
For the exam at GCSE, you mainly need to know:
- What “universal gate” means (NAND or NOR can implement any other gate)
- Why NAND and NOR are significant (manufacturers can build entire circuits from one gate type)
Completing a multi-gate truth table
A three-input circuit with multiple gates requires 8 rows (2³). Follow this method:
Step 1: Set up input columns. Column A: repeat 0,0,0,0,1,1,1,1. Column B: repeat 0,0,1,1,0,0,1,1. Column C: repeat 0,1,0,1,0,1,0,1.
Step 2: Work through the circuit left to right. Calculate intermediate wire values as separate columns.
Example: A AND B → result X. X OR C → final output.
| A | B | C | X = A AND B | Output = X OR C |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 |
Always add intermediate columns — examiners give credit for correct intermediate values even if the final output has a mistake.
Drawing a circuit from a Boolean expression
This is a skill that separates higher-grade students. The method:
- Read the expression from right to left (find the final gate first)
- Identify inputs to that final gate
- Work backwards until you reach the primary inputs A, B, C
Example: Draw a circuit for (A AND B) OR (NOT C)
- Final gate: OR
- Left input to OR: A AND B (one AND gate)
- Right input to OR: NOT C (one NOT gate on C)
- Total gates: AND, NOT, OR
Draw: A and B into an AND gate → output to left side of OR gate. C into a NOT gate → output to right side of OR gate. OR gate output = final output.
Exam technique
For truth table questions:
- Start with the input columns — use the binary counting pattern
- Add an intermediate column for each gate in the circuit
- Never jump to the final output column without showing your working
- Marks are usually awarded per column, not just for the final answer
For “draw a circuit” questions:
- Label all inputs clearly (A, B, C)
- Label the output
- Use correct gate symbols (the examiner will expect the standard British BS symbols)
- Every gate input must connect to something — no floating wires
For “state one advantage of NAND being a universal gate”:
- “An entire logic circuit can be implemented using only NAND gates, meaning manufacturers only need to produce one type of gate component, reducing manufacturing complexity and cost.”
Practice with the interactive tool
Use the Logic Gate Simulator on this site to:
- Toggle inputs and verify truth table rows instantly
- Build multi-gate circuits
- Check your drawn circuits match the expected truth table
And try the question bank for past-paper style logic gate questions with full mark schemes.