HW _ 5 Solutions

HW 5 Solutions - QM METHOD 1 Find minimum sum-of-products solution using QM procedure f(a b c d = m 2,3,4,7,9,11,12,13,14 d(1,10,15 Group 1

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QM METHOD 1. Find minimum sum-of-products solution using QM procedure + = ) 15 , 10 , 1 ( ) 14 , 13 , 12 , 11 , 9 , 7 , 4 , 3 , 2 ( ) , , , ( d m d c b a f Group Minterms ABCD Minterms ABCD Minterms ABCD 1 0001 1,3 00-1 1,3,9,11 -0-1 PI 2 2 0010 1,9 -001 1,9,3,11 - 0 - 1 1 4 0100 2,3 001- 2,3,10,11 -01- PI 3 3 0011 2,10 -010 2,10,3,11 - 01 - 9 1001 4,12 -100 PI 1 3,7,11,15 --11 PI 4 10 1010 3,7 0-11 3,11,7,15 -- 11 2 12 1100 3,11 -011 9,11,13,15 1--1 PI 5 7 0111 9,11 10-1 9,13,11,15 1 -- 1 11 1011 9,13 1-01 10,11,14,15 1-1- PI 6 13 1101 10,11 101- 12,13,14,15 11-- PI 7 3 14 1110 10,14 1-10 12,14,13,15 11 -- 4 15 1111 12,13 110- 12,14 11-0 7,15 -111 11,15 1-11 13,15 11-1 14,15 111- PI Chart Reduced Chart 9 13 14 PI 2 X PI 5 X X PI 6 X PI 7 X X Even though PI 5 covers more minterms than PI 2 in the ‘Recuded Chart’ , looking back at the ‘PI Chart’ , we see that they both cover the same amount of minterms. Therefore:

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This note was uploaded on 10/28/2010 for the course EEN 304 taught by Professor Nigeljohn during the Spring '10 term at University of Miami.

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HW 5 Solutions - QM METHOD 1 Find minimum sum-of-products solution using QM procedure f(a b c d = m 2,3,4,7,9,11,12,13,14 d(1,10,15 Group 1

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