EECS270-W08-HW1-Solutions-v2

# EECS270-W08-HW1-Solutions-v2 - EECS 270 Winter 2008...

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EECS 270 Winter 2008 Homework 2 Solutions Problem 1 (8 points) – Vahid Problem 2.12 Evaluate the Boolean equation F = a AND (b OR c) AND d for the given values of a, b, c, and d: a) a=1, b=1, c=0, d=1 b) a=0, b=0, c=0, d=1 c) a=1, b=0, c=0, d=0 d) a=1, b=0, c=1, d=1 a) F = 1 · (1 + 0) · 1 = 1 b) F = 0 · (0 + 0) · 1 = 0 c) F = 1 · (0 + 1) · 0 = 0 d) F = 1 · (0 + 1) · 1 = 1 Problem 2 (12 points) – Vahid Problems 2.26 & 2.27 Use algebraic manipulation to convert the following equations to sum-of-products form: a) F = a(b + c)(d’) + ac’(b + d) b) F = a’b(c + d’) + a(b’ + c) + a(b + d)c a) F = a(b + c)(d’) + ac’(b + d) = abd’ + acd’ + abc’ + ac’d using the Distributive Law (and also the Commutative Law to reorder literals) b) F = a’b(c + d’) + a(b’ + c) + a(b + d)c = a’bc + a’bd’ + ab’ + ac + abc + acd using the Distributive Law = a’bc + a’bd’ + ab’ + ac(1 + b + d) using the Distributive Law again = a’bc + a’bd’ + ab’ + ac(1) using the Identity Law = a’bc + a’bd’ + ab’ + ac using the Identity Law again 1

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(20 points) – Vahid Problem 2.71 Design a 3x8 decoder with enable using AND, OR, and NOT gates. 2
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## This homework help was uploaded on 04/04/2008 for the course EECS 270 taught by Professor Hayes during the Winter '08 term at University of Michigan.

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EECS270-W08-HW1-Solutions-v2 - EECS 270 Winter 2008...

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