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## Karnaugh map

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**A**B AB C AB CD 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 A 0 1 00 01 11 10 00 01 11 10 0 1 0 1 0 1 00 01 11 10 0 1 Karnaugh map • Karnaugh map allows viewing the function in a picture form • Map is arranged such that two neighbors differ in only one variable • It is easy to identify what terms can be combined • Two terms must be “adjacent” in the map • Example: 1, 2, 3, and 4 variables maps are shown below**AB**C AB C 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 00 01 11 10 00 01 11 10 0 1 0 1 Adder truth tables, functions, and K-map S = A’B’Cin + A’BCin’ + AB’Cin’ + ABCin Cout = BCin + ACin + AB**XY**Z XY ZW 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 00 01 11 10 00 01 11 10 0 1 00 01 11 10 Farmer’s example truth tables and K-maps • With three variables, we do not want X and Y or Y and Z to be equal (both 0 or both 1) at the same time • With four variables, it is not a problem if W is also the same F1 = X’Y’ + YZ + XZ’ F2 = X’ZW’+XYW’+Y’Z’W