Boolean Logic and Expressions

Boolean Logic · 5 question types

Practise

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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 three representations of a Boolean function can be converted in any direction. Each conversion has been covered above, but it helps to see them together.

From → to	Method (covered in)
Circuit → expression	Label each gate's output with its sub-expression, working left to right (section 3).
Truth table → expression	One AND term per `Q = 1` row, OR them together (section 4).
Expression → truth table	Evaluate the expression for every possible combination of inputs (section 5, repeated for each row).
Expression → circuit	One gate per operator; bracket innermost first; NOT gates before the negated signal feeds its next gate (covered in topic 26).
Circuit → truth table	Trace signals through each gate for every input row, adding intermediate columns (covered in topic 26).
Truth table → circuit	Derive the expression from the truth table, then draw the circuit for that expression.

The circuit below can be taken either way: label each gate's output to build the Boolean expression for X, or trace every input combination through the gates to fill in its truth table.

Three-input logic circuit with inputs A, B and C: A and B feed a NAND gate then a NOT gate, B and C feed a NOR gate, and the two branches feed a final OR gate that produces output X. — Source: Logic Expressions by Save My Exams

Whatever route the exam asks for, the key check is the same: at the end, the truth table of the new representation must agree with the truth table of the original, row for row.