
4.3 INTRODUCTION TO LOGIC FUNCTION GRAPHICS 137
to Eqs. (4.8) and (4.9), there results
f +
¯
f =
m(0, 2, 5, 6) +
m(1, 3, 4, 7)
=
m(0, 1, 2, 3, 4, 5, 6, 7)
=1.
Generally, the Boolean sum of all 2
n
minterms of a function is logic 1 according to
2
n
−1
i=0
m
i
= 1. (4.10)
Similarly, by using the AND law, X ·
¯
X = 0, and the AND form of the commutative laws,
there results
f ·
¯
f =
M(1, 3, 4, 7) ·
M(0, 2, 5, 6)
=
M(0, 1, 2, 3, 4, 5, 6, 7)
=0.
Or generally, the Boolean product of all 2
n
maxterms of a function is logic 0 according to
2
n
−1
i=0
M
i
= 0. (4.11)
Equations (4.10) and (4.11) are dual relations by the definition of duality given in Subsection
3.10.2.
To summarize, the ...