6 Synthesis of Majority Expressions Through Primitive Function Manipulation
151
Table 6.15 Vector v updated
from X 1 , for the second loop
example
Minterms f X 1 v
0
0 0
0
1
0 0
0
2
1 0
0
3
0 0
0
4
1 1
1
5
0 1
−1
6
1 1
1
7
1 1
1
8
1 0
0
9
0 0
0
10
0 0
0
11
1 0
0
12
0 1
−1
13
1 1
1
14
1 1
1
15
1 1
1
16
0 0
0
17
0 0
0
18
0 0
0
19
0 0
0
20
0 1
−1
21
0 1
−1
22
0 1
−1
23
0 1
−1
24
0 0
0
25
0 0
0
26
0 0
0
27
0 0
0
28
0 1
−1
29
0 1
−1
30
0 1
−1
31
0 1
−1
We have X 3 = M(M(A, D, 0), M(B, C, 0), M(A, B, E)), covering the
minterms {2, 3, 6, 7, 8, 10, 11, 14}.
With the selection of X 3 , MP C returns M(X 1 , X 2 , X 3 ) = M(C, M(M(C, D, 1),
M(B, E, 0), M(A, B, E)), M(M(A, D, 0), M(B, C, 0), M(A, B, E))) as output,
which has less inverters than its dual form.