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150 CHAPTER 4/LOGIC FUNCTION REPRESENTATION AND MINIMIZATION

to be an EPI, the other OPI becomes redundant (an RPI). In similar fashion a minimum
POS cover is extracted as shown in Fig. 4.18b, giving the result

- - - - f (A + B + C) )
Zp OS = (A + B + CKB + C + D)(A+B + D~)\ (A + D), (4.27)
^ (B + L + D) J

which is seen to have four dyads (including one of two OPIs) and one quad. The maxterm
MO can be looped out in two ways (dashed loops in Fig. 4.18b) to form the OPI dyads
A/(12, 13) and Af (5, 13) represented by the bracketed s-terms in Eq. (4.27).

4.4.3 Incompletely Specified Functions: Don't Cares
In the design of logic circuits nonessential minterms or maxterms may be introduced so as
to simplify the circuit. Such nonessential minterms or maxterms are called don 't cares and
are represented by the symbol

0 = Min/Max = don't care.

Thus, the don't care can be taken as logic 0 or logic 1, take your choice. The symbol 0 can
be thought of as a logic 0 with a logic 1 superimposed on it.
Don't cares can arise under the following two conditions:

• When certain combinations of input logic variables can never occur, the output
functions for such combinations are nonessential and are assigned don't cares.
• When all combinations of input logic variables occur but certain combinations
of these variables are irrelevant, the output functions for such combinations are
assigned don't cares.

As an example of the second condition, the BCD number system discussed in Subsection
2.4.1 has 10 4-bit binary patterns for decimal integers 0 through 9. Thus, there are six 4-bit
patterns, representing decimal integers 10 through 15 that are never used — that is, we
"don't care" about them. Accordingly, the don't care symbol 0 can be assigned to any
output generated by one of the six nonessential 4-bit patterns. This will be demonstrated in
Subsection 6.5.2 for conversion from BCD to XS3 decimal codes.
Consider the three- variable function

/(A, fi, C)= ^m(l,3,4,7) + 0(2,5)
4 28
Nonessential ( - )
minterms
(don't cares)
written in canonical SOP form showing essential minterms and nonessential minterms (don't
cares). The K-maps representing minimum SOP and POS cover are shown in Figs. 4.19a
and 4.19b, giving the results

F SOP=AB + C
(4.29)