Truth table

A truth table is the exhaustive tabular representation of a Boolean function — a complete mapping from all possible input combinations to their corresponding outputs. For a function with n binary inputs, the table contains 2^n rows, each row representing one input state and displaying the output value. Truth tables are computationally profligate but conceptually indispensable: they make explicit the extensional content of a logical expression, stripping away syntactic variation to reveal the pure input-output relationship. The transformation from truth tables to minimal Boolean expressions — via methods like the Quine-McCluskey algorithm or Karnaugh maps — is one of the foundational problems of digital design, and the size of a truth table (2^n rows) is the reason that logic synthesis is inherently exponential in the worst case.