EE2301Dis4F09Sol

EE2301Dis4F09Sol - Department of Electrical and Computer...

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1 Department of Electrical and Computer Engineering University of Minnesota EE 2301 Fall 2009 Introduction to Digital System Design L. L. Kinney Discussion IV Solutions 10/1-2: Topics are a design example, minimization and Karnaugh maps. 1. A = A 1 A 0 and B = B 1 B 0 are two 2-bit, unsigned binary numbers. The function F(A 1 , A 0 , B 1 , B 0 ) is 1 if A < B and is 0 otherwise. (a) Construct a Truth Table for the function F. (b) Give the minterm expansion expression for F. (c) Using the simplification identity, algebraically find all prime implicants of F. (a) A 1 A 0 B 1 B 0 F 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 0 (b) F(A 1 , A 0 , B 1 , B 0 ) = A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 (c) F(A 1 , A 0 , B 1 , B 0 ) = A 1 A 0 B 0 + A 1 A 0 B 1 + A 1 B 1 B 0 + A 1 B 1 B 0 + A 0 B 1 B 0 + A 1 A 0 B 1 = A 1 A 0 B 0 + A 1 B 1 + A 1 B 1 + A 0 B 1 B 0 = A 1 A 0
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