Boolean algebra

Boolean algebra is the math of true and false — or, in a computer, 1 and 0. Instead of adding and multiplying numbers, you combine yes/no facts using just three operations: AND, OR and NOT. Think of a porch light wired to two switches: AND means the light glows only when both switches are on; OR means either one is enough; NOT simply flips a switch's answer to its opposite.

George Boole worked this out in the 1850s, long before computers existed. Decades later engineers realised those same true/false rules describe circuits perfectly, since a wire is either carrying voltage (1) or not (0). Today every chip is a vast pile of AND, OR and NOT gates. Boolean algebra lets designers write down what a circuit should do, then shrink that into fewer gates — for example proving "A AND A" is just "A," saving transistors and power.