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.

Examiners accept several equivalent notations. Knowing all of them protects against losing marks for "wrong-looking" answers.

Operator	Word form	Algebraic form	Other accepted forms
AND	`A AND B`	`A · B`	`AB`, `A ∧ B`
OR	`A OR B`	`A + B`	`A ∨ B`
NOT	`NOT A`	`¬A`	`A̅` (overbar), `A'`
NAND	`A NAND B`	`¬(A · B)`	`(A · B)'`, overbar over the bracket
NOR	`A NOR B`	`¬(A + B)`	`(A + B)'`, overbar over the bracket
XOR	`A XOR B`	`A ⊕ B`	`(A · ¬B) + (¬A · B)`

A few important conventions:

The dot · for AND is often dropped, just like in ordinary algebra. So AB means "A AND B", and AB + C means (A AND B) OR C.
+ here means OR, not numerical addition. 1 + 1 in Boolean algebra is 1, not 2.
An overbar over a variable (or group of variables) means NOT. Many printed mark schemes use the overbar; handwritten answers usually use ¬ or ' instead.
Variables are always single letters, usually A, B, C, ..., with output Q, P, X or Z.

(highest to lowest): brackets → NOT → AND → OR.

This mirrors school algebra: brackets first, then unary −, then ×, then +. As in algebra, brackets remove all ambiguity, so when in doubt, add brackets.