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An example Karnaugh map. Note: Every rectangle encloses 2, 4 or 8 trues or 1's. Also, the yellows rectangle wraps off the top and encloses the two bottom right cells. A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression.
Those 16 numbers correspond to the minterms of Image:K-map minterms.svg used in a 4-variable [[:en:Karnaugh map File usage No pages on the English Wikipedia use this file (pages on other projects are not listed).
English: A 4 variable, 4x4 Karnaugh map. Date: 22 December 2006: Source: Own work This W3C-unspecified vector image was created with Inkscape. Author: en:User:Cburnett:
While this example was simplified by applying normal algebraic methods [= (′ +)], in less obvious cases a convenient method for finding minimal PoS/SoP forms of a function with up to four variables is using a Karnaugh map. The Quine–McCluskey algorithm can solve slightly larger problems.
In his 1952 paper "A Chart Method for Simplifying Truth Functions", [2] Veitch described a graphical procedure for the optimization of logic circuits, which is referred to as Veitch chart. A year later (in 1953), the method was refined in a paper by Maurice Karnaugh [3] into what became known as Karnaugh map (K-map) or Karnaugh–Veitch map (KV ...
In Chapter 6, section 6.4 "Karnaugh map representation of Boolean functions" they begin with: "The Karnaugh map 1 [1 Karnaugh 1953] is one of the most powerful tools in the repertory of the logic designer. ... A Karnaugh map may be regarded either as a pictorial form of a truth table or as an extension of the Venn diagram." [13] (pp 103–104)
The following 16 pages use this file: Algebraic normal form; Beta normal form; Blake canonical form; Canonical normal form; Conjunctive normal form; Disjunctive normal form
In Boolean algebra, Petrick's method [1] (also known as Petrick function [2] or branch-and-bound method) is a technique described by Stanley R. Petrick (1931–2006) [3] [4] in 1956 [5] [6] for determining all minimum sum-of-products solutions from a prime implicant chart. [7]