Going the Other Way: Writing the Expression for a Circuit — Logic Gates and Circuits | IGCSE Computer Science

Exam Frequency Analysis

Past paper frequency (2018 to 2024)

This topic accounts for approximately 9% of your exam marks.

stable

Medium

Stable9%

Truth tables and Boolean expressions from circuit diagrams appear in every paper. 4 to 6 marks.

Sometimes a question gives the circuit and asks for the Boolean expression. The method is the mirror image of section 8.

Method. (1) Label each gate's output left to right. (2) Write the expression for each labelled output in terms of the inputs feeding it. (3) Substitute into the final output's expression so that everything is expressed in terms of the original inputs.

Example — the circuit has an OR gate with inputs A and B whose output feeds a NOT gate. The NOT gate's output is Q.

The OR gate's output is A OR B. Call it P.
The NOT gate's output is NOT P, i.e. NOT (A OR B).
So Q = NOT (A OR B).

Notice that this gives the same truth table as a NOR gate, which is exactly why NOR is defined as "NOT OR".