Page 186 - Engineering Digital Design

4.5 MULTIPLE OUTPUT OPTIMIZATION 157

CD
AB\ 00 01 ' 11 10
00
Shared Plsfor1yf 2
01 ABD
BCD
11
12 13 15 ABC
A
10
11 10/

(a)
CD C \ CD
I
AB\ 00 01 '1 1 10 ' AB\ 00 01 ' 11 10
w
00 1 00
0 3 2 0
01 (1 T) 01
4 5 7 6

11 ( 1 1 O 11
12 ' * 13 15 14 12 13 15
10 n, 10 11 10/
9
* 11 10
/f,
(b)
FIGURE 4.26
Multioutput SOP optimization for the system represented by Eqs. (4.36) and Fig. 4.24. (a) K-map
and shared Pis for f\ -fa . (b) K-maps showing optimal SOP cover for functions f\ and fi.

Optimized SOP Cover. ANDing the canonical SOP forms of Eqs. (4.36) by using the
ANDing rules given by Eqs. (4.32) produces

m 0
/, • / 2 = X! ( ' 6, 1, 8, 12, 14) + 0(13).
The K-map for /i • / 2 and the table of shared p-term Pis is given in Fig. 4.26a. The K-maps
in Fig. 4.26b show the optimized cover for the two-function system. The results are

f 2=ABC + ABC

which represent a combined gate/input tally of 1 / 19 making use of only one of the three
shared Pis. Here, shared PI dyads ABD and BCD are rejected in favor of quads AB and CD
in the f\ and /2 K-maps, respectively. Notice that function f\ is not an individual minimum,
but combined with the individual minimum for function /2 results in an optimized system.
An individual minimum for function f\ is achieved by replacing the shared PI m(6, 1) with
the quad m(6, 1, 14, 15) in Fig. 4.26b. When combined with the individual minimum for
function / 2, there results a gate/input tally of 8/21, which is not optimal. Also, note that