Karnaugh map
method to simplify boolean algebra expressions; refinement of Edward Veitch's 1952 Veitch diagram
A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced the technique in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which itself was a rediscovery of Allan Marquand's 1881 logical diagram or Marquand diagram. They are also known as Marquand–Veitch diagrams, Karnaugh–Veitch (KV) maps, and (rarely) Svoboda charts. An early advance in the history of formal logic methodology, Karnaugh maps remain relevant in the digital age, especially in the fields of logical circuit design and digital engineering.
Definition
A Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability. It also permits the rapid identification and elimination of potential race conditions.
The required Boolean results are transferred from a truth table onto a two-dimensional grid where, in Karnaugh maps, the cells are ordered in Gray code, and each cell position represents one combination of input conditions. Cells are also known as minterms, while each cell value represents the corresponding output value of the Boolean function. Optimal groups of 1s or 0s are identified, which represent the terms of a canonical form of the logic in the original truth table. These terms can be used to write a minimal Boolean expression representing the required logic.
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