Page 222 - Engineering Digital Design

PROBLEMS 193

4.18 Following the discussion in Section 4.6, compress each function in Problem 4.8 into
a third-order K-map (Map Key = 2) and extract minimum SOP and POS cover. Use
the LSB variable as the entered variable (EV).

4.19 Following the discussion in Section 4.7, compress each of the following five-variable
functions into a fourth-order K-map (Map Key = 2) and extract minimum SOP and
POS cover. Use the LSB variable as the entered variable (EV).
(a) q(A, B, C, D, E) = 0 M(0, 1, 2, 5, 14, 16, 17, 18, 19, 21, 26, 27, 30)
(b) r(A, B, C, D, E) = ABCE + ACDE + BCDE + ABCE + ABDE
+ A BCDE + BCDE + ABD + BCD + ABCDE
(c) s(A, B, C, D, E) = £m(0, 2, 4, 5, 7, 10, 13, 15, 21, 23, 24, 25, 28, 29, 30)
(d) t(A,B,C, D) = (A + B+_D+E)(B + C + D + E)(A+B+E)(A + C + D+E)
•(B + C + D)(B + C+D + E)(A +B+C+D+ E\B + C + D + E)
• (A + B + C)(B + C + D}(B + C + D + E)
4.20 Minimize each function of Problem 4.19 in both SOP and POS by using a conventional
(1's and O's) K-map. To do this follow the example in Fig. 4.56.
4.21 Following the discussion in Section 4.6, compress each function in Problem 4.2 into
a first-order K-map (Map Key = 4) and extract a minimum SOP and POS expression
for each. Use the last two significant bit variables as EVs.
4.22 Following the discussion in Section 4.6, compress each function in Problem 4.3 into a
second-order K-map (Map Key = 4) and extract a minimum SOP and POS expression
for each. Use the last two significant bit variables as EVs.
4.23 Following the discussion in Section 4.6, compress each function in Problem 4.7 into
a first-order K-map (Map Key = 4) and extract a minimum SOP and POS expression
for each. Use the last two significant bit variables as EVs.

4.24 Following the discussion in Section 4.6, compress each function in Problem 4.8 into a
second-order K-map (Map Key = 4) and extract a minimum SOP and POS expression
for each. Use the last two significant bit variables as EVs.
4.25 Compress each function in Problem 4.19 into a third-order K-map (Map Key = 4) and
extract a minimum SOP and POS expression for each. Use the last two significant bit
variables as EVs.
4.26 Shown in Fig. P4.3 are two functions, F and Z, each of four variables, that have
been compressed into third-order K-maps. (Hint: It will help to first simplify the

\BC \BC 01 11 10
A\ oo 01 11 10 AX °°
*5 0 D 0 0 1 D fflD
*
0 1 W D 1 D(*D) ^D+D (h
^
/
(a) (b)
FIGURE P.4.3