Transcription of ECE-223, Solutions for Assignment #2
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ECE-223, Solutions for Assignment #2
ECE-223, Solutions for Assignment #2. Chapter 2, Digital Design, M. Mano, 3rd Edition ). Simplify the following Boolean expression to a minimum number literals: a) xy + xy . b) (x + y)(x + y ). c) xyz + x y + xyz . d) (A+B) (A +B ) . a) xy + xy = x ( y+y )= = x b) (x+y)(x+y ) = xx + xy + yx+yy = x + xy + xy + 0 = x (1+ y + y) = x Also (x+y)(x+y ) =x+ yy = x + 0 = x c) xyz + x y + xyz = xy(z+z ) + x y = xy +x y = y(x+x )=y d) (A+B) (A +B ) = (A B ).(AB) = 0. ). Simplify the following Boolean expression to a minimum number literals: a) ABC + A B + ABC . b) x yz + xz c) (x+y) (x +y ). d) xy + x(wz + wz ). e) (BC +A D)(AB +CD ). a) ABC + A B + ABC = AB(C+C ) + A B = AB + A B = B(A+A ) = B. b) x yz + xz = z(x y+x)= z(x +x)(x+y) = z(x+y). c) (x+y) (x +y ) = x y .(x +y ) = x y +x y = x y . d) xy + x(wz + wz ) = xy + xw(z+z ) = xy + xw = x(y+w). e) (BC +A D)(AB +CD )= AB BC + AB A D + CD BC + CD A D = 0. ). Find the complement of the following expressions: a) xy +x y b) ( AB +C)D +E.
Page: 1 ECE-223, Solutions for Assignment #2 Chapter 2, Digital Design, M. Mano, 3rd Edition 2.2) Simplify the following Boolean expression to a minimum number literals:
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