Boolean algebra models digital signals using two values: 0 (LOW) and 1 (HIGH). These rules help simplify a logic expression before implementing its circuit.

Essential identities

• Identity: A + 0 = A and A · 1 = A
• Complement: A + A′ = 1 and A · A′ = 0
• Idempotent: A + A = A and A · A = A

Universal gates

NAND and NOR are universal gates: either gate type can be combined to construct NOT, AND, OR, and any Boolean function.

Try it

Simplify A + A·B. The absorption law gives A + A·B = A. Verify the result by checking both possible values of A.