Page 175 - Engineering Digital Design
P. 175
146 CHAPTER 4/LOGIC FUNCTION REPRESENTATION AND MINIMIZATION
\CD
AB\ 00 01 (... 10
11
:U i
00 )
1
/^— — r^ \
01 (— X ^
11 <-*<>
n
10
FIGURE 4.14
Minimum cover (shaded) by using the loop-out protocol avoids the redundant quad (dashed loop).
forbidden groups are presented in Fig. 4.15, which has been "crossed out" to indicate that
such groupings are not allowed.
4.4.1 Examples of Function Minimization
Just as canonical forms can be read from a K-map in two ways (SOP and POS), so also can
a function be read from a K-map in either minimum SOP form or minimum POS form. To
illustrate, consider the function
G(A, X,Y ) = ^2 m(0, 3, 5, 7), (4.23)
which is mapped and minimized in Fig. 4.16. Noting that the I's are looped out as two
dyads and a monad as are the O's, there results
GSOP = AXY + XY + AY (minimum SOP cover)
\
\
\
\
\
/
/ \
/. . . . ^_A.
L/^
//
/
FIGURE 4.15
Examples of forbidden (non-2") groupings of minterms and maxterms.
