Evaluating a Boolean Expression for Given Inputs — Boolean Logic and Expressions | IGCSE Computer Science

Exam Frequency Analysis

Past paper frequency (2018 to 2024)

This topic accounts for approximately 6% of your exam marks.

stable

Low

Stable6%

Writing Boolean expressions from logic diagrams and simplifying using laws appear regularly.

The reverse problem: you are given an expression and specific values for its variables, and have to compute the output.

Method. (1) Substitute each variable with its given 0 or 1. (2) Apply operators in precedence order: brackets first, then NOT, then AND, then OR. (3) Write down every intermediate value rather than doing the whole thing in your head.

Example — evaluate Q = A · B + ¬C when A = 1, B = 0, C = 1.

Substitute: Q = 1 · 0 + ¬1.

Now apply in precedence order:

¬1 = 0 (NOT goes before AND or OR).
1 · 0 = 0 (AND goes before OR).
0 + 0 = 0 (OR is last).

So Q = 0.

Example — evaluate Q = (A + B) · (¬B + C) when A = 0, B = 1, C = 0.

Substitute: Q = (0 + 1) · (¬1 + 0).

Brackets first. Inside the first bracket: 0 + 1 = 1. Inside the second bracket: ¬1 = 0, then 0 + 0 = 0.
Now combine: 1 · 0 = 0.

So Q = 0.

Two reliable sanity checks while evaluating:

An AND with any 0 input is 0, no matter what the other inputs are.
An OR with any 1 input is 1, no matter what the other inputs are.

If you spot one of these mid-calculation, you can stop early; in the exam, still write the final answer with the intermediate values shown, so you collect the method marks.