ic
Section 8.3 Minimization
667
In four-variable maps, when two adjacent squares are marked with 1, one
variable can be eliminated; when four adjacent squares are marked with 1,
two variables can be eliminated; when eight adjacent squares are marked with
1, three variables can be eliminated.
Figure 8.24 illustrates some instances of two adjacent marked squares, Figure 8.25
illustrates some instances of four adjacent marked squares, and Figure 8.26 shows
instances of eight.
1
1
1
1
1
1
1
1
x 1 x 2
x 3
x 1 xЈ 2
xЈ 3
xЈ 1 xЈ 2 xЈ 1 x 2
x 1 x 2
x 3 x 4
x 1 xЈ 2
x 3 xЈ 4
xЈ 1 xЈ 2
xЈ 3 xЈ 4
xЈ 1 x 2
xЈ 3 x 4
figure 8.24
xЈ 3 xЈ 4
1
1
1
1
1
1
1
1
x 1 x 2
x 3 x 4
x 1 xЈ 2
x 3 xЈ 4
xЈ 1 xЈ 2
xЈ 3 xЈ 4
xЈ 1 x 2
xЈ 3 x 4
x 1 x 2
x 3 x 4
x 1 xЈ 2
x 3 xЈ 4
xЈ 1 xЈ 2 xЈ 1 x 2
xЈ 3 x 4
1
1
1
1
x 1 x 2
x 3
x 1 xЈ 2
xЈ 3
xЈ 1 xЈ 2 xЈ 1 x 2
1
1
1
1
x 1 x 2
x 3
x 1 xЈ 2
xЈ 3
xЈ 1 xЈ 2 xЈ 1 x 2
figure 8.25
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
x 1 x 2
x 3 x 4
x 1 xЈ 2
x 3 xЈ 4
xЈ 1 xЈ 2
xЈ 3 xЈ 4
xЈ 1 x 2
x 1 x 2
x 1 xЈ 2 xЈ 1 xЈ 2 xЈ 1 x 2
xЈ 3 x 4
x 3 x 4
x 3 xЈ 4
xЈ 3 xЈ 4
xЈ 3 x 4
figure 8.26