Boolean algebra works with variables that take values zero or one. Useful laws include identity, complement, idempotence, absorption and distributivity. In this article, + means OR, juxtaposition means AND, and NOT means inversion; these are logical operations rather than ordinary arithmetic.
Worked example
Simplify F = A + AB. Factor A to obtain A(1 + B). Because 1 OR B is always 1, the result is A. A truth-table check agrees: when A is zero both terms are zero; when A is one the output is already one.
What to watch for
Do not apply ordinary arithmetic subtraction or division to Boolean expressions. Boolean 1 + 1 equals 1, because + denotes OR.
Try it yourself
Simplify A(A + B).
Answer: Distribute to obtain AA + AB = A + AB = A. This is the other absorption law.
How to study this topic
Read one operation at a time and use parentheses generously. Check a simplification with every truth-table row, not just a convenient example. A useful simpler expression must preserve the complete specified function.
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