Page 215 - A Practical Guide from Design Planning to Manufacturing

188 Chapter Six

XY XY
00 01 11 10 00 01 11 10
0 1 1 0 1 0 1 0 0 1
Z Z
1 0 0 0 1 1 0 1 0 0
A = XZ + XY B = YZ + XYZ
Figure 6-13 Three-variable examples.

top and bottom rows are considered neighbors (Fig. 6-14). For example,
F is a neighbor of F and F is a neighbor of F .
4
8
0
6
In the first example in Fig. 6-15, all the 1’s are covered by one set of
two cells and two sets of four cells. Sets of eight cells are possible by com-
bining two neighboring sets of four. The second example uses two sets
of four. One set includes all the center cells, whereas the other contains
all four corners. Because cells at the edges of the map are considered
neighbors of cells on the opposite side, it is possible to create a set of four
out of all the corner cells.
Karnaugh maps can be used with five variable functions by creating
2 four-variable maps, which differ by just one input. Cells in the exact
same position in the two maps are considered neighbors. For six vari-
able functions, 4 four-variable maps are needed. Arranged in two rows
and columns, cells are neighbors with cells in the same position in the

W X Y Z F
0 0 0 0 F 0
0 0 0 1 F 1
0 0 1 0 F 2
0 0 1 1 F 3
0 1 0 0 F 4 WX
0 1 0 1 F 5 00 01 11 10
00 F F F F
0 1 1 0 F 6 0 4 12 8
01 F F F F
0 1 1 1 F 7 YZ 1 5 13 9
11 F F F F
1 0 0 0 F 8 3 7 15 11
10 F 2 F 6 F 14 F 10
1 0 0 1 F 9
1 0 1 0 F 10
1 0 1 1 F 11
1 1 0 0 F 12
1 1 0 1 F 13 Figure 6-14 Four-variable
1 1 1 0 F 14 Karnaugh map.
1 1 1 1 F 15