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Converting a Karnaugh map to a Zhegalkin polynomial. The figure shows a function of three variables, P(A, B, C) represented as a Karnaugh map, which the reader may consider as an example of how to convert such maps into Zhegalkin polynomials; the general procedure is given in the following steps:
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 [ 1 ] [ 2 ] as a refinement of Edward W. Veitch 's 1952 Veitch chart , [ 3 ] [ 4 ] which itself was a rediscovery of Allan Marquand 's 1881 logical diagram [ 5 ] [ 6 ] or Marquand diagram . [ 4 ]
Minimizing Boolean functions by hand using the classical Karnaugh maps is a laborious, tedious, and error-prone process. It isn't suited for more than six input variables and practical only for up to four variables, while product term sharing for multiple output functions is even harder to carry out. [10]
Although more practical than Karnaugh mapping when dealing with more than four variables, the Quine–McCluskey algorithm also has a limited range of use since the problem it solves is NP-complete. [ 22 ] [ 23 ] [ 24 ] The running time of the Quine–McCluskey algorithm grows exponentially with the number of variables.
Digital Circuits/Karnaugh Maps; Usage on en.wikiversity.org Digital Electronics/Lecture Karnaugh Map Reductions; Usage on eu.wikipedia.org Lankide:PrietoI/Proba orria; Karnaughen mapa; Usage on fa.wikipedia.org جدول کارنو; Usage on gl.wikipedia.org Diagrama de Venn; Usage on it.wikipedia.org Mappa di Karnaugh; Bell Laboratories; Usage ...
The k-map visually shows where race conditions occur in the minimal expression by having gaps between minterms, for example, the gap between the blue and green rectangles. If the input were to change from 1110 {\displaystyle 1110} [ 1 ] to 1010 {\displaystyle 1010} then a race will occur between B C D ¯ {\displaystyle BC{\overline {D ...
Simultaneous transitions in multiple finite-state machines can be shown in what is effectively an n-dimensional state-transition table in which pairs of rows map (sets of) current states to next states. [1] This is an alternative to representing communication between separate, interdependent finite-state machines.
"For more than three variables, the basic illustrative form of the Venn diagram is inadequate. Extensions are possible, however, the most convenient of which is the Karnaugh map, to be discussed in Chapter 6." [13] (p 64) In Chapter 6, section 6.4 "Karnaugh map representation of Boolean functions" they begin with: