Truth tables

2.4.1 Boolean Logic

Boolean Logic — Note 2 of 4

Knowledge of the truth tables for each logic gate; Understanding of how to create, complete or edit truth tables for given scenarios

What you need to know

A truth table shows the output of a Boolean expression for every possible combination of inputs. For two inputs (A and B) there are four possible combinations (00, 01, 10, 11). Truth tables are essential for understanding, debugging, and designing logic circuits. You must know the truth tables for AND, OR, and NOT gates.

What to know

AND truth table: 0 AND 0 = 0, 0 AND 1 = 0, 1 AND 0 = 0, 1 AND 1 = 1.
OR truth table: 0 OR 0 = 0, 0 OR 1 = 1, 1 OR 0 = 1, 1 OR 1 = 1.
NOT truth table: NOT 0 = 1, NOT 1 = 0.
For n inputs, a truth table has 2^n rows (e.g. 2 inputs = 4 rows, 3 inputs = 8 rows). Formula: rows = 2^n.
A truth table shows all possible inputs to a logic circuit AND the associated/dependent output for each combination of inputs.
You can use 0/1 or True/False or T/F notation in exams.

Exam technique

Tip:When asked 'describe the purpose of a truth table', say it shows 'all possible inputs AND the output for each input'. Just saying 'all possible combinations of inputs and outputs' only gets 1/2 marks — you must say the output DEPENDS ON the inputs.
Tip:When asked how many rows, use 2^n. For P = (A OR B) AND NOT C, there are 3 inputs so 2^3 = 8 rows.
Tip:To identify a gate from a truth table: if output is 1 only when BOTH inputs are 1 → AND. If output is 1 when ANY input is 1 → OR.

Example:P = NOT(A AND B) → work it out step by step: first evaluate A AND B, then apply NOT. Results: (0,0)→1, (0,1)→1, (1,0)→1, (1,1)→0.

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