hw2solutions-complete

hw2solutions-complete - GEORGIA INSTITUTE OF TECHNOLOGY...

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GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2030 Fall 2005 Problem Set #2 SOLUTION Assigned: 12-Sep-05 Due Date: 19-Sep-05 This assignment is due at the beginning of class on Monday, September 19. Problem 1 (2 pts): Use Boolean algebra only to derive the sum-of-minterm expression for the following binary func- tions. Please sort the terms in your answer so that they are in increasing minterm index order. (Do not use truth tables.) (a) F = ( a + b ) c b = ( ab ) c b = ab c or = m 6 (b) F = c + ( c + a ) b = c + b c + a b = c ( a + a )( b + b ) + ( a + a ) b c + a b ( c + c ) = abc + a b c + a bc + a b c + ab c + a b c + a bc + a b c = a b c + a b c + a bc + a b c + ab c + abc or = X m (1 , 2 , 3 , 5 , 6 , 7) (c) F = ( a b ) c = ( a b + a b ) c = ( a b + a b ) c + ( a b + a b ) c = ( a b c + a b c ) + (( a b )( a b )) c = ( a b c + a b c ) + ( a + b )( a + b ) c = a b c + a b c + a ac + a b c + abc + b b c = a b c + a b c + a b c + abc

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= a b c + a b c + a b c + abc or = X
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hw2solutions-complete - GEORGIA INSTITUTE OF TECHNOLOGY...

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