Boolean Algebra Basics

The mathematics of two-state signals.

Boolean algebra works with variables that can only be 0 or 1. Its three basic operations are AND, written as a dot, OR, written as a plus, and NOT, shown as a bar or prime. Each corresponds to a logic gate in digital hardware.

The algebra has laws just like ordinary algebra, plus some unusual ones. Identity, null, idempotent, complement, commutative, associative and distributive laws let you rewrite an expression into a simpler but equivalent form.

• AND is 1 only when all inputs are 1.
• OR is 1 when at least one input is 1.
• NOT flips its input.

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