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Unit 4 Solutions
F(A, B, C, D) = ∑ m(3, 4, 5, 8, 9, 10, 11, 12, 14)
F = A’B’CD + A’BC’D’ + A’BC’D + AB’C’D’ +
AB’C’D + AB’CD’ + AB’CD + ABC’D’ + ABCD’
4.30 (a) 4.30 (b) F(A, B, C, D) = ∏ M(0, 1, 2, 6, 7, 13, 15)
F = (A + B + C + D)(A + B + C + D’)
(A + B + C’ + D)(A + B’ + C’ + D)
(A + B’ + C’ + D’)(A’ + B’ + C + D’)
(A’ + B’ + C’ + D’)
4.32 (a) If don’t cares are changed to (1, 1), respectively,
A B C D E F Z
0 0 0 1 1 X20
4.33 1 These truth table entries
were made don’t cares
4.32 (b) If don’t cares are changed to (1, 0), respectively
4.32 (c) If don’t cares are changed to (1, 1), respectively
F3 = (A + B + C) (A + B + C’) = A + B
4.32 (d) If don’t cares are changed to (0, 1), respectively
F4 = A’B’C’ + A’BC + AB’C’ + ABC
= B’C’ + BC
G2(A, B, C) = ∑ m(0, 1, 6, 7) = ∏ M(2, 3, 4, 5)
4.34 (a) G1(A, B, C) = ∑ m(0, 7) = ∏ M(1, 2, 3, 4, 5, 6) 4.34 (b)
f(A,B,C,D) = AB+ A’CD = ABC’D’ + ABC’D
+ ABCD’ + ABCD + A’B’CD + A’BCD
= (A+A’CD)(B+A’CD) = (A+C)(A+D)(A’+B)
(B+C)(B+D)
f(A,B,C,D) = (A+B’+C+D’)(A+B’+C+D)
4.29 (a) f(A,B,C,D) = (A+B+D’)(A’+C)(C+D)
= (A+B+D’)(A’D+C) = AC+A’BD+BC+CD’
= AC(B+B’)(D+D’)+A’BD(C+C’)
+BC(A+A’)(D+D’)+(A+A’)(B+B’)CD’
= ABCD+ABCD’+AB’CD+AB’CD’+A’BCD
4.29 (b)