Karnaugh map

A Karnaugh map (K-map) is a graphical method for simplifying Boolean expressions by exploiting adjacency in the space of binary input combinations. Invented by Maurice Karnaugh in 1953 as a refinement of the Veitch diagram, the K-map arranges the rows of a truth table in a grid where geometrically adjacent cells differ by exactly one bit — a Gray code ordering that makes visually apparent which minterms can be merged to eliminate variables. For functions of up to four or six variables, the K-map remains an elegant pedagogical tool that reveals the topological structure of Boolean space; for larger functions, it is superseded by algorithmic methods like the Quine-McCluskey procedure and modern logic synthesis software. The K-map's enduring value lies not in its practical utility for contemporary chip design but in its demonstration that logical simplification is fundamentally a problem of spatial pattern recognition — a bridge between discrete algebra and visual geometry.