0984

Boolean Logic and Expressions

Boolean Logic · 5 question types

Practise

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.

Given a circuit, the safest method is to label each gate's output with its Boolean sub-expression, working from the inputs through to the final output.

Method. (1) Identify each gate and the signals feeding it. (2) Working left to right, write the output of each gate as a Boolean sub-expression using its input labels. (3) Use that sub-expression as the input to any gate it feeds. (4) The final gate's output is the expression for Q.

Logic circuit with inputs A and B feeding an OR gate whose output is labelled (A+B), this output and input C then feeding an AND gate whose output is labelled C·(A+B), showing how each gate's output is written as a Boolean sub-expression.
Source: Logic circuit to Boolean expression by Save My Exams

A second circuit to work through: label the OR gate's output P, and the following NOT gate then gives the final output Q.

Logic circuit with inputs A and B feeding an OR gate whose output is labelled P, P then feeding a NOT gate whose output is labelled Q, illustrating how to label each gate's output while writing the expression for Q.
Source: Logic Expressions by Save My Exams
Exam tip

Writing a logic expression for a circuit (do not simplify)

What comes up: you are given a logic circuit and asked to write the logic expression for its output (often worth around four marks).

Write: label the output of each gate as a Boolean sub-expression, working left to right from the inputs; feed each sub-expression into the next gate it connects to, so that the final gate's output becomes the whole expression for the output (Q or X). Any accepted notation scores: a dot or nothing for AND (A·B or AB), + for OR, and an overbar, ¬ or ' for NOT.

Watch out: the paper almost always tells you "do not simplify" — write the expression exactly as the circuit is wired, gate for gate, keeping the brackets that match how the gates are grouped. Simplifying is not asked for, earns no extra marks, and risks introducing an error that costs the marks you had already secured.