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4.2 SOP AND POS FORMS 135

POS Term Binary Decimal M, POS Term Binary Decimal M i

A+B+C+D 0000 0 M A+B+C+D 1000 8 M 8
o
A+B+C+D 0001 1 M 1 A+B+C+D 1001 9 M 9
A+B+C+D 0010 2 A+B+C+D 1010 10
M 2
M
10
A+B+C+D 0011 3 M 3 A+B+C+D 1011 11 M n
A+B+C+D 0100 4 M 4 A+B+C+D 1100 12 M 12
A+B+C+D 0101 5 M 5 A+B+C+D 1101 13 M 13
A+B+C+D 0110 6 M 6 A+B+C+D 1110 14 M 14
A+B+C+D 0111 7 M 7 A+B+C+D 1111 15 M 1S

FIGURE 4.3
Maxterm code table for four variables.

revealing a complementary relationship between minterms and maxterms. The validity of
Eqs. (4.6) is easily demonstrated by the following examples:

m 5 = ABC =

and
=A+B + C + D=ABCD = m ]2,

where use has been made of DeMorgan's laws given by Eqs. (3.15a).
A function whose terms are all maxterms is said to be given in canonical POS form as
indicated next by using maxterm code.

C)-(A + B + C)-(A + B + C)
001 101 100 000
= M\ • MS • A/4 • MO
, 1,4,5)

Note that the operator symbol J~] is used to denote the ANDing (Boolean product) of max-
terms MO, MI , M 4, and M 5.
Expansion of a reduced POS function to canonical POS form can be accomplished as
indicated by the following example:

f(A, B,C) = (A + C)(B + C)(A + B + C)
= (A+BB + C)(AA + B + C)(A +B + C)

= (A + B + C)(A + B + C)(A +B + C)(A +B + C)(A + B + C)
M 3 MI MI MI M4
,4,7). (4.7)

Here, use is made of multiple applications of the distributive, AND, and OR laws in the