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What (who) is McCluskey algorithm - definition
![[[Hasse diagram]] of the search graph of the algorithm for 3 variables. Given e.g. the subset <math>S = \{abc, a\overline{b}c, \overline{a}bc, \overline{a}b\overline{c}, \overline{a}\overline{b}c \}</math> of the bottom-level nodes (light green), the algorithm computes a minimal set of nodes (here: <math>\{ \overline{a}b, c \}</math>, dark green) that covers exactly <math>S</math>.](https://commons.wikimedia.org/wiki/Special:FilePath/QmcSearchGraph3 Ab+c svg.svg?width=200 "[[Hasse diagram]] of the search graph of the algorithm for 3 variables. Given e.g. the subset <math>S = \{abc, a\overline{b}c, \overline{a}bc, \overline{a}b\overline{c}, \overline{a}\overline{b}c \}</math> of the bottom-level nodes (light green), the algorithm computes a minimal set of nodes (here: <math>\{ \overline{a}b, c \}</math>, dark green) that covers exactly <math>S</math>.")
Wikipedia
The Quine–McCluskey algorithm (QMC), also known as the method of prime implicants, is a method used for minimization of Boolean functions that was developed by Willard V. Quine in 1952 and extended by Edward J. McCluskey in 1956. As a general principle this approach had already been demonstrated by the logician Hugh McColl in 1878, was proved by Archie Blake in 1937, and was rediscovered by Edward W. Samson and Burton E. Mills in 1954 and by Raymond J. Nelson in 1955. Also in 1955, Paul W. Abrahams and John G. Nordahl as well as Albert A. Mullin and Wayne G. Kellner proposed a decimal variant of the method.
The Quine–McCluskey algorithm is functionally identical to Karnaugh mapping, but the tabular form makes it more efficient for use in computer algorithms, and it also gives a deterministic way to check that the minimal form of a Boolean function has been reached. It is sometimes referred to as the tabulation method.
The method involves two steps:
- Finding all prime implicants of the function.
- Use those prime implicants in a prime implicant chart to find the essential prime implicants of the function, as well as other prime implicants that are necessary to cover the function.
