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194 CHAPTER 4 / LOGIC FUNCTION REPRESENTATION AND MINIMIZATION

\CD
AB\ 00 01 11 10
00 1 0 0 1

01 1 1 0 0
11 0 1 1 0

10 1 0 0 1
/F
FIGURE P.4.4

subfunctions in cells 4 and 7 of function Z by applying the laws of Boolean algebra
while treating the 0 as an entered variable.)
(1) By following the example in Fig. 4.33a, construct the first-order submap for each
of the eight cells in each K-map.
(2) Give the canonical SOP and POS expressions in code form for each function.
(3) Extract the minimum SOP and POS forms from each third-order K-map, keeping
in mind the discussion on the use of don't cares in Subsection 4.6.1.
4.27 Compress the fourth-order K-map in Fig. P4.4 into a second-order K-map (Map
Key = 4) and loop out minimum SOP and POS expressions according to the follow-
ing format:
(a) Set A, B as the axis variables.
(b) Set B, C as the axis variables.
(c) Set A, C as the axis variables.
4.28 Compress the following function into a fourth-order K-map (Map Key = 4) and extract
minimum SOP and POS forms. By using the gate/input tally (exclusive of inverters),
indicate which form is simpler.
Y(A, B, C, D, E,F) = M(0, 1, 5, 7, 9, 15, 16, 18, 21, 24, 29, 31, 35, 37, 39,
40,45,49,50,56,58,60,61,63)

4.29 Shown in Fig. P4.5 is a function of six variables that has been compressed into a
third-order K-map, hence a third-order compression (Map Key = 8).

\BC
A\ 00 01 11 10
1 X+Y X-Y Z

1 XT 0 Z

/ F
FIGURE P.4.5