6 Synthesis of Majority Expressions Through Primitive Function Manipulation
143
Table 6.10 List of set G for
n = 3
Classic function Majority function
A · B
M(A, B, 0)
A · B
M(A, B, 0)
A · B
M(A, B, 0)
A · B
M(A, B, 1)
A · C
M(A, 0, C)
A · C
M(A, 0, C)
A · C
M(A, 0, C)
A · C
M(A, 1, C)
B · C
M(0, B, C)
B · C
M(0, B, C)
B · C
M(0, B, C)
B · C
M(1, B, C)
A + B
M(A, B, 1)
A + B
M(A, B, 1)
A + B
M(A, B, 1)
A + B
M(A, B, 0)
A + C
M(A, 1, C)
A + C
M(A, 1, C)
A + C
M(A, 1, C)
A + C
M(A, 0, C)
B + C
M(1, B, C)
B + C
M(1, B, C)
B + C
M(1, B, C)
B + C
M(0, B, C)
Table 6.11 List of set T for
n = 3
Classic function
Majority function
AB + AC + BC
M(A, B, C)
A · B + A · C + B · C M(A, B, C)
A · B + A · C + B · C M(A, B, C)
A · B + A · C + B · C M(A, B, C)
A · B + A · C + B · C M(A, B, C)
A · B + A · C + B · C M(A, B, C)
A · B + A · C + B · C M(A, B, C)
A · B + A · C + B · C M(A, B, C)
variables, considering three inputs per combination. Note that each combination has
eight variations of inverters and, for n = 3, there is only one possible combination.
|T | = t · 8
(6.10)
Table 6.11 shows the list of functions in T , for n = 3.