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PROBLEMS 191

A(H)
B(H) Combinational
C(H) Logic
f,(H)
D(H)
FIGURE P.4.1

4.8 The following four- variable functions are incompletely specified functions — they
contain don't cares. Use a conventional (1 's and O's) K-map to minimize each function
in both SOP and POS form and, with the help of the gate/input tally (exclusive of pos-
sible inverters), indicate which is simpler. Also, identify any OPIs that may be present.
(a) E(a,b,c,d) = ^m(6, 11,12, 13, 14) + 0(0, 1, 2, 3, 4, 5)
(b) F(A,B,C, D) = Y[M(0,3,6, 11, 13, 15) • 0(5, 8, 10, 14)
(c) G(W, X, Y, Z) = £>(0, 4, 6, 8, 9, 10, 11, 14, 15) + 0(1, 5)
(d) H(w, x, v, z) = PI M(l, 2- 3, 9, 10, 14) • 0(11, 13)
(e) I(A, B, C, D) = £ m(4, 5, 7, 12, 14, 15) + 0(3, 8, 10)
(f) J(a, b, c,d} = ]\ M(0, 1, 2, 5, 7, 9) • 0(4, 6, 10, 13)
4.9 Find the optimum cover (either SOP or POS) for the following four-input/two-output
system (see Fig. P4.1). Base your choice on the total gate/input tally (including in-
verters) for the system. Assume the inputs and outputs are all active high. Do not
construct the logic circuit.

fi=2_; m(Q, 2, 4, 5, 9, 10, 11, 13, 15)

/ 2 = J^m(2, 5, 10, 11, 12, 13, 14, 15)

4.10 Three functions, each of three inputs, are given in canonical SOP form. Follow the
discussion in Section 4.5 and find the optimized SOP minimum for the three func-
tions taken as a system. Give the total gate/input tally for the system, exclusive of
inverters.
/i(A,B,C) = y^m(l,3,5,6,7)

(0, 1,3,6)

4.11 Two functions, each of four variables, are given in canonical SOP form. Follow the
discussion in Section 4.5 and find the optimized SOP and POS minima for the two
functions taken as a system. By using the gate/input tally, exclusive of inverters,
indicate which is simpler, the SOP result or the POS result.

2 5 6
7 8 10 14 15
m
F,(A, B, C, D) = £ < ' ' ' ' ) + #(!' ' ' )
F 2(A, fl, C, D) = /n(l, 5, 7, 8, 11, 14, 15) + 0(2, 3, 10)