chap18 - ECEn/CS 224 Chapter 18 Homework Solutions 18.1...

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Last updated: 12/15/2006 ECEn/CS 224 Chapter 18 Homework Solutions 18.1 Plot the following function on a KMap and identify a minimum POS solution for it. Then, solve it a second time using hazard-free minimization. Show your work. F(A,B,C,D) = m0 + m1 + m2 + m4 + m5 + m6 + m9 + m11 + m13 + m15 The there are two minimum POS solutions to this minterm expansion. These two minimum solutions are shown in the K-maps below. AB CD 00 01 11 10 00 1 1 01 1 1 1 1 11 1 1 10 1 1 AB CD 00 01 11 10 00 1 1 01 1 1 1 1 11 1 1 10 1 1 F 1 (A,B,C,D) = A’D’ + AD + A’C’ F 2 (A,B,C,D) = A’D’ + AD + C’D To make either of these hazard free, we must add redundant prime implicants such that all adjacent 1s in the K-map are covered by an implicant. We will mark the redundant implicants we add with red, dashed boxes. AB CD 00 01 11 10 00 1 1 01 1 1 1 1 11 1 1 10 1 1 AB CD 00 01 11 10 00 1 1 01 1 1 1 1 11 1 1 10 1 1 F 1 (A,B,C,D) = A’D’ + AD + A’C’ + C’D F 2 (A,B,C,D) = A’D’ + AD + C’D +
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chap18 - ECEn/CS 224 Chapter 18 Homework Solutions 18.1...

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