What Is a Truth Table?

A truth table enumerates every possible combination of boolean inputs and records the output of a logical expression for each. With two inputs there are four combinations — (0,0), (0,1), (1,0), (1,1) — and each operation produces a distinct pattern across them. That pattern is the operation's complete definition.

Reading the Key Operations

AND lights up only on (1,1). OR lights up everywhere except (0,0). XOR lights up on the two mixed rows. NAND and NOR are the exact inverses. The implication A → B is the famously counter-intuitive one: false only when the premise holds and the conclusion fails, which gives it three true rows.

From Truth Tables to Circuits

Every digital device is built from logic gates whose behavior is specified by truth tables: AND, OR, NOT, NAND, NOR, XOR, and XNOR. Complex circuits — adders, memory, processors — are designed by combining these primitives, and boolean algebra simplifies the results. Understanding the four-row tables here is the first step into that world.