Digital Electronics
Boolean algebra is the mathematics of writing logic expressions like equations and simplifying them — George Boole founded it in 1854, and today it underlies every processor. Variables take only 0 and 1. The basic rules are intuitive: A·1 = A, A·0 = 0, A+0 = A, A+1 = 1. Also A·A = A, A + A = A (idempotent) and A·Ā = 0, A + Ā = 1 (complement).
The most powerful tool is De Morgan’s laws: taking the inverse of a group "flips" the operations. (A·B)̄ = Ā + B̄ and (A+B)̄ = Ā · B̄. So a NAND is really an "OR with inverted inputs", and a NOR an "AND with inverted inputs". This is the key to rebuilding a circuit with only NAND or only NOR gates.
Distribution works just like in ordinary algebra: A·(B+C) = A·B + A·C. The absorption rule A + A·B = A shortens expressions. Example: A·B + A·B̄ = A·(B + B̄) = A·1 = A — two terms collapse to one variable. For larger expressions, Karnaugh maps make this simplification visual; fewer gates = a cheaper, faster, lower-power circuit.
⚡ Open this lesson in the simulator — free