Page 196 - Engineering Digital Design

4.7 FUNCTION REDUCTION OF FIVE OR MORE VARIABLES 167

ACEF

BCDEF

FIGURE 4.37
An A/B|| CD/EF format for the six-variable function of Eq. (4.51) and Fig. 4.36a, showing minimum
SOP cover.

Notice that the SOP form of the equivalence function, EQF = EF + EF given by Eq. (3.5),
is used in cell 5 to extract minimum cover in minterm code and that the POS form (E + F}
• (E + F) is required for extraction of minimum cover in max term code. Note also that the
loop-out protocol is applied first to the EVs and then to the 1's (in minterm code) and O's
(in maxterm code) as "clean-up" operations. This protocol procedure is recommended to
avoid possible redundancy.
There are other K-map formats that can be used to extract reduced or minimum cover
for a given function. Consider again the six-variable function given in Eq. (4.51). Presented
in Fig. 4.37 is the A/B \\ CD/EF format for the conventional (1's and O's) mapping of this
function where only minterm code extraction is considered. Observe that extraction of the
EPIs takes on a three-dimensional (3-D) character in a 2-D layout, which can be somewhat
perplexing.
As a final example, the format of Fig. 4.37 is used to deal with the following incompletely
specified function of eight variables:
Z(a, b, c, d, e, /, S, T} = ^ ™(16, 18, 20, 22, 24, 26, 28, 30, 48, 50, 52, 54, 56, 58, 60,
62, 98,99, 102, 103, 106, 107, 110, 111, 160-191,
225-227, 229-231, 233-235, 237-239,
241, 243, 245-247, 248, 250, 252,254, 255)
+ 0(0-15, 32-47, 64-79, 112-159, 192-207). (4.53)