Karnaugh Map

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 …show more content…

Perhaps the hardest-to-visualize wrap-around term is which covers the four corners—this covers minterms 0, 2, 8, 10.
[edit] Solution
Once the Karnaugh Map has been constructed and the groups derived, the solution can be found by eliminating extra variables within groups using the axioms of boolean algebra. It can be implied that rather than eliminating the variables that change within a grouping, the minimal function can be derived by noting which variables stay the same.
For the Red grouping: * The variable A maintains the same state (1) in the whole encircling, therefore it should be included in the term for the red encircling. * Variable B does not maintain the same state (it shifts from 1 to 0), and should therefore be excluded. * C does not change: it is always 0. Because C is 0, it has to be negated before it is included (thus, ). * D changes, so it is excluded as well.
Thus the first term in the Boolean sum-of-products expression is
For the Green grouping we see that A and B maintain the same state, but C and D change. B is 0 and has to be negated before it can be included. Thus the second term is
In the same way, the Blue grouping gives the term
The solutions of each grouping are combined into:
[edit] Inverse
The inverse of a function is solved in the same way by grouping the 0s instead.
The three terms to cover the inverse are all shown with grey boxes with different colored borders: * brown— * gold— *