🔗 Paper 1 · Topic 2: Boolean Logic
2.3b Truth Tables & Boolean Expressions
Edexcel 1CP2 · GCSE Computer Science · ~15 min read · 🔒 Pro
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Boolean Expressions

A Boolean expression is a mathematical expression that produces a TRUE or FALSE result. These use Boolean operators to combine inputs.

  • NOT A — written as Ā or NOT A
  • A AND B — written as A · B or A AND B
  • A OR B — written as A + B or A OR B
  • A XOR B — written as A ⊕ B

Expressions can be combined: (A AND B) OR (NOT C)

Building Truth Tables for Expressions

To build a truth table for a multi-gate expression, work through it column by column, calculating intermediate values at each stage.

📝 Example: (A AND B) OR (NOT A)

Step 1: List all input combinations (2 inputs = 4 rows)

Step 2: Calculate intermediate columns: A AND B then NOT A

Step 3: Calculate final output: (A AND B) OR (NOT A)

ABA AND BNOT A(A AND B) OR (NOT A)
00011
01011
10000
11101

Three-Input Truth Tables

With 3 inputs (A, B, C), there are 2³ = 8 rows. Always list inputs in binary counting order:

ABCExample: A AND B AND C
0000
0010
0100
0110
1000
1010
1100
1111

Reading Logic Circuit Diagrams

Exam questions often show a logic gate diagram and ask you to complete the truth table or identify the Boolean expression. Steps:

  • Identify each gate and its inputs
  • Work left to right, calculating each gate's output
  • The final gate's output is the circuit's output
  • Fill in intermediate columns for partial marks

De Morgan's Laws

These two rules are important for simplifying Boolean expressions:

  • NOT (A AND B) = (NOT A) OR (NOT B)
  • NOT (A OR B) = (NOT A) AND (NOT B)

In other words: NAND = NOT-AND = (NOT A) OR (NOT B) and NOR = NOT-OR = (NOT A) AND (NOT B).

Exam tip: For multi-gate circuits, always add intermediate columns. Examiners award marks for each correct column, not just the final output. State your working clearly and follow the binary counting pattern for rows (000, 001, 010, 011...).
⚠️ Common Mistakes
  • Skipping intermediate columns — always show working
  • Listing inputs in the wrong order — use binary counting (0,0 → 0,1 → 1,0 → 1,1)
  • Mixing up De Morgan's laws: NOT(A AND B) ≠ NOT A AND NOT B
  • Confusing XOR and OR when A=B=1
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Worksheet — 2.3b Truth Tables & Boolean Expressions

8 Edexcel-style questions · instantly marked

Q1How many rows are in a truth table with 3 inputs?[1]
✅ Mark scheme
8 rows [1]. With n inputs, there are 2ⁿ rows.
Q2Write the Boolean expression for: "output is 1 only when A is 1 AND B is 0".[2]
✅ Mark scheme
A AND (NOT B) [1] or A · B̄ [1]. Accept equivalent notation.
Q3Complete the truth table for (NOT A) AND B: rows A=0,B=0; A=0,B=1; A=1,B=0; A=1,B=1.[4]
✅ Mark scheme
A=0,B=0: NOT A=1, output=0 [1]; A=0,B=1: NOT A=1, output=1 [1]; A=1,B=0: NOT A=0, output=0 [1]; A=1,B=1: NOT A=0, output=0 [1].
Q4State De Morgan's law for NOT(A AND B).[1]
✅ Mark scheme
NOT(A AND B) = (NOT A) OR (NOT B) [1].
Q5Evaluate (A OR B) AND (NOT C) when A=1, B=0, C=1.[3]
✅ Mark scheme
A OR B = 1 OR 0 = 1 [1]; NOT C = NOT 1 = 0 [1]; 1 AND 0 = 0 [1]. Output = 0.
Q6What does it mean to work "column by column" when filling in a truth table?[2]
✅ Mark scheme
Calculate intermediate outputs one gate at a time [1]; fill in each intermediate column fully before moving to the next column [1].
Q7State De Morgan's law for NOT(A OR B).[1]
✅ Mark scheme
NOT(A OR B) = (NOT A) AND (NOT B) [1].
Q8What is the output of (A XOR B) OR (A AND B) when A=1, B=1?[3]
✅ Mark scheme
A XOR B = 1 XOR 1 = 0 [1]; A AND B = 1 AND 1 = 1 [1]; 0 OR 1 = 1 [1]. Output = 1.
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Mini Test — Truth Tables & Expressions

Timed exam-style test.

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