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4.8 MINIMIZATION ALGORITHMS AND APPLICATION 171

ABC- - / 0,1,2,3 AB- - 00-- -
AB-- D / 0,1,8,9 -1 C-- -- 0 0 --
A--C D / 0,2,1,3 A D —

-BC D / 0,2,4,6 A --- 6 0--- 0
AB- D / 0,4,2,6 A -- - D
-BC D / 0,0,1,9 - DC- -

ABC " /
A - C D /
AB-- D /
ABC - /
6,14(8) -BC D 6,14 -BC D

14,15(1) ABC - 14,15 ABC -
/ Indicates that an implicant is covered by a Prime Implicant in the columns to the right.
FIGURE 4.42
Determination of Pis for the 1's in the function Y of Eq. (4.55).

To do this, the O's of Eq. (4.58) will be treated as 1's, as required by the Q-M algorithm,
to yield Fpos in minimum SOP form. Then, application of DeMorgan's law, given by
Eqs. (3.15), yields the results FPQS = FPOS by involution. Here, the 0's in Eq. (4.58) are
treated as essential minterms, not as nonessential maxterms. Shown in Fig. 4.44 is the tabu-
lar determination of Pis for the O's, treated as 1 's, in the maxterm form of function F given
by Eq. (4.58).
The final step is to tabulate the Pis of Fig. 4.44 with the maxterms (now treated as
minterms) in Eq. (4.58) to obtain the EPIs for the function F POs- This is done in Fig. 4.45,

\° 1 4 6 8 14 15 Essential Pis

Els
0,1,2,3 / /
0,1,8,9 / / / -- B C -- = B C

0,2,4,6 / / / A---- D = A D
6,14 / /
14,15 / / ABC - = ABC
FIGURE 4.43
Table of Pis (from Fig. 4.42) vs minterms for the function Y of Eq. (4.55) showing the resulting EPIs.