Logic Gates

Logic gates are the physical atoms of digital computation — elementary devices that implement the operations of Boolean algebra by mapping binary inputs to binary outputs according to determinate truth tables. A logic gate is where abstract logical structure becomes concrete electrical behavior: voltages above a threshold represent 1, voltages below represent 0, and the gate's circuitry enforces the mapping regardless of the continuous physics that implements it.

The functional completeness of the AND-OR-NOT set means that any computable logical function, no matter how complex, can be constructed by composing these three gate types. This compositionality is the engineering secret of digital systems: a billion-transistor processor is, at the level of logical description, merely an elaborate arrangement of gates. The physical substrate — whether semiconductor transistors, electromechanical relays, or optical switches — is interchangeable so long as the threshold behavior is preserved. The gate abstracts away the physics, and in doing so makes digital architecture possible.