IGCSE · Practice questions · Completing truth tables

Eight rows, no slips.

Six original Cambridge-style questions on completing truth tables for two and three inputs, with every row worked out.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Keep these straight

Inputs, working, output.

Rows: 2ⁿ of them, in binary counting order 000 to 111.
Working columns: one for the output of each gate, from the inputs towards X.
Statements: write the expression first, taking care with which value means NOT.
Check: pick two rows and trace them through the circuit again.

Calculate

[4 marks]

Complete the truth table for X = (A OR B) AND NOT C, for the inputs 000 to 111 in binary order.

Rows 000, 001: 0, 0. ✓
Rows 010, 011: 1, 0. ✓
Rows 100, 101: 1, 0. ✓
Rows 110, 111: 1, 0. ✓

Trace

[4 marks]

A logic circuit has a NAND gate with inputs A and B. Its output and input C go into an XOR gate, whose output is X. Complete the truth table for X.

A NAND B is 1, 1, 1, 1, 1, 1, 0, 0 (working column). ✓
Rows 000 to 011: X = 1, 0, 1, 0. ✓
Rows 100, 101: X = 1, 0. ✓
Rows 110, 111: X = 0, 1. ✓

Apply

[4 marks]

A machine M starts (M = 1) when the safety guard is closed (G = 1) and either start button P or start button Q is pressed (= 1). (a) Write the logic expression. (b) Complete the truth table for inputs G, P, Q.

(a) M = G AND (P OR Q). ✓
(b) Rows 000 to 011: 0, 0, 0, 0. ✓
Row 100: 0. ✓
Rows 101, 110, 111: 1, 1, 1. ✓

Explain

[2 marks]

Explain why a truth table for a circuit with three inputs has eight rows, and why the rows are written in binary counting order.

Each input has two possible values, so there are 2 × 2 × 2 = 8 combinations. ✓
Counting from 000 to 111 makes sure every combination appears once, with none missed or repeated. ✓

Analysis

[2 marks]

A student completes the truth table for X = A AND NOT B and writes X = 0, 1, 0, 0 for the rows A B = 00, 01, 10, 11. Identify the error and give the correct output column.

The student has worked out NOT A AND B (or applied the NOT to the wrong input). ✓
Correct: NOT B is 1 only when B = 0, so X = 0, 0, 1, 0. ✓

Calculate

[4 marks]

Complete the truth table for X = (A AND B) OR (B AND C). Use working columns.

A AND B: 0, 0, 0, 0, 0, 0, 1, 1. ✓
B AND C: 0, 0, 0, 1, 0, 0, 0, 1. ✓
X: 0, 0, 0, 1, 0, 0, 1, 1. ✓
X = 1 in rows 011, 110 and 111 only. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.