Karnaugh Map Essay

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Karnaugh map
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For former radio station KMAP (1962-1968) in Dallas-Fort Worth, see KRLD-FM.

An example Karnaugh map
The Karnaugh map (K-map for short), Maurice Karnaugh's 1953 refinement of Edward Veitch's 1952 Veitch diagram, is a method to simplify Boolean algebra expressions. The Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability, permitting the rapid identification and
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They are usually indicated on the map with a dash or X.
The example to the right is the same above example but with minterm 15 dropped and replaced as a don't care. This allows the red term to expand all the way down and, thus, removes the green term completely.
This yields the new minimum equation:

Note that the first term is just A not . In this case, the don't care has dropped a term (the green); simplified another (the red); and removed the race hazard (the yellow as shown in a following section).
Also, since the inverse case no longer has to cover minterm 15, minterm 7 can be covered with rather than with similar gains.
[edit] Race hazards
[edit] Elimination

Above k-map with the term added to avoid race hazards
Karnaugh maps are useful for detecting and eliminating race hazards. Race hazards are very easy to spot using a Karnaugh map, because a race condition may exist when moving between any pair of adjacent, but disjointed, regions circled on the map. * In the example to the right, a potential race