2.9. Karnaugh-map or K-map
K-map is the best tool for minimization of five or fewer variables functions for humans. K-maps are
graphic and require pattern-matching which is one of human’s strongest abilities. Many believe that
humans solve problems by creative pattern-matching.
K-map is a number of squares which are labeled using reflective gray code (each code is only 1
change from an adjacent code). For a given square, the user enters 0 or 1 corresponding to the
function value at the inputs represented by the labels. Here are K-map examples for 2, 3, and 4 Variables: Each of the squares will contain a 1 if the function is 1 (min-term locations) and 0 otherwise. You
may also use “-“, which reflects the “don’t care” (can be 0 or 1, whichever gives us the lowest
Literal Count, LC).The Literal Count (LC) is proportional to the number of gates needed during the implementation,
so the less the better. Here is the location of each min-term on a Karnaugh-Map:0 1
2 3
0 1
0
1
F(A,B)=AB
2-VariablesB
A 0 1
2 3
0 1
00
01
11
10
F(A,B,C)
3-VariablesC
AB
6 7
4 5
0 1
4 5
00 01 11 10
00
01
11
10
F(A,B,C,D)
4-VariablesCD
AB
3 2
7 6
12 13 15 14
8 9 11 10
A B C D Min-term,m
0 0 0 0 0
0 0 0 1 1
0 0 1 0 2
0 0 1 1 3
0 1 0 0 4
0 1 0 1 5
0 1 1 0 6
0 1 1 1 7
1 0 0 0 8
1 0 0 1 9
1 0 1 0 10
1 0 1 1 11
1 1 0 0 12
1 1 0 1 13
1 1 1 0 14
1 1 1 1 15F(A,B)
2-VariablesF(A,B,C)
3-VariablesF(A,B,C,D)
4-Variables