Boolean Expressions and Simplification

A Boolean expression is an algebraic expression that uses Boolean operators (AND, OR, NOT) to describe the output of a logic circuit or condition. In GCSE Computer Science, you need to be able to write, interpret and simplify Boolean expressions.

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Writing Boolean Expressions

Notation

Operation	Common Notations	Example
NOT	¬A, A̅, NOT A	¬A
AND	A ∧ B, A · B, A AND B	A ∧ B
OR	A ∨ B, A + B, A OR B	A ∨ B
XOR	A ⊕ B, A XOR B	A ⊕ B

Operator Precedence (Order of Operations)

Just like in mathematics where multiplication is done before addition, Boolean algebra has an order of operations:

1. Brackets — evaluate expressions inside brackets first
2. NOT — negation is applied next
3. AND — conjunction is applied next
4. OR — disjunction is applied last

So the expression A ∨ B ∧ C is evaluated as A ∨ (B ∧ C) — the AND is done before the OR.