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 1 A 00 01 11 10 AB CD C
0 1 B

2. Adder truth tables, functions, and K-map1 AB C 1 AB C
S = A’B’Cin + A’BCin’ + AB’Cin’ + ABCin
Cout = BCin + ACin + AB

3. 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 1 00 01 11 10 XY ZW 1 XY Z
F1 = X’Y’ + YZ + XZ’
F2 = X’ZW’+XYW’+Y’Z’W