hw8_soln - ECE3060 Homework #8 due Thursday October 19 @...

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ECE3060 November 1, 2006 Homework #8 due Thursday October 19 @ 4:30pm 100 points Solutions 1. (20) Consider the following function: f = a’b’c’d’ + a’b’c’d + a’b’cd’ + a’b’cd + ab’c’d + ab’cd’ + abc’d’ + abc’d + abcd’. Use your favorite method to derive all possible prime implicants for f. For full credit, state which method you are using, show all work and explain your work. Also, state how many essential prime implicants you have found. Using K-MAP method: 7 prime implicants: a’b’, b’cd’, acd’, abd’, abc’, ac’d, b’c’d 1 essential prime implicant : a’b’ (since a’b’c’d’ and a’b’cd are only covered by a’b’) 2. (5) Design an A matrix for your answer to problem 1 above. each row is a minterm of the function. each column is a different prime implicant of the fuction. if a minterm (row) is covered by a prime implicant (column), then that element is a 1 a'b’ b’cd’ acd’ abd’ abc’ ac’d b’c’d a’b’c’d’ 1 0 0 0 0 0 0 a’b’c’d 1 0 0 0 0 0 1 a’b’c d’ 1 1 0 0 0 0 0 a'b’c d 1 0 0 0 0 0 0 a b’c’d 0 0 0 0 0 1 1 a b’c d’ 0 1 1 0 0 0 0 a b c’d’ 0 0 0 1 1 0 0 a b c’d 0 0 0 0 1 1 0 a b c d’ 0 0 1 1 0 0 0
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3. (35) For the following A matrix, use the Quine-McCluskey Exact 2-Level Logic Minimization algorithm taught in class to find the global minimum number of prime implicants such that all minterms are covered. Shown are the rows labeled m
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hw8_soln - ECE3060 Homework #8 due Thursday October 19 @...

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