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ECE320_HomeWork_No_2

# ECE320_HomeWork_No_2 - EE 320 Homework No 2(Solution 1 A 0...

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EE 320 - Homework No. 2 (Solution) 1. A B C AB BC AB’ BC’ A+C AB+(BC)’ (AB)’(A+C)’ AB’+BC’ 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 (a) (b) (c) 2. a) (A+B)’(A’+B’)’ = A’B’(A.B) = A.A’.BB’ = 0 b) X+XY+XZ = X(1+Y+Z) = X.1=X c) X+X’Y+(XY)’ = X+X’Y+X’+Y’ = X+X’+X’Y+Y’ = 1+X’Y+Y’ = 1 3. a) F(A,B,C,D) = D(A’+B)+B’D = A’D+BD+B’D = A’D(B+B’) + BD(A+A’) + B’D(A+A’) = A’BD + A’B’D + ABD + AB’D = A’BD(C+C’) + A’B’D(C+C’) + ABD(C+C’) + AB’D (C+C’) = A’BCD + A’BC’D + A’B’CD + A’B’C’D + ABCD + ABC’D + AB’CD + AB’C’D = Σ(1,3,5,7,9,11,13,15) S.O.P. = (0,2,4,6,8,10,12,14) P.O.S. b) F(A,B,C) = (A’+B)(B’+C) = (A’+B+CC’)(B’+C+AA’) = (A’+B+C)(A’+B+C’)(A+B’+C)(A’+B’+C) = (2,4,5,6) = Σ(0,1,3,7) c) F(X,Y,Z) = (XY+Z)(Y+XZ) = (X+Z)(Y+Z)(X+Y) = (X+Z+YY’)(Y+Z+XX’)(X+Y+ZZ’) = (X+Y+Z)(X+Y’+Z)(X’+Y+Z)(X+Y+Z’) = (0,1,2,4) = Σ(3,5,6,7)

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EE 320 - Homework No. 2 (Solution) 4. a) F(W,X,Y,Z) = Σ(0,2,8,9,10,11,14,15) Y YZ WX 00 01 11 10 00 1 1 1 X 11 1 1 W 10 1 1 1 1 S.O.P.: F = WX’ + WY + X’Z’ Z Y YZ WX 00 01 11 10 00 0 0 01 0 0 0 0 X 0 0 11 W P.O.S.: 10 F’ = XW’ + ZW’ + XY’
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ECE320_HomeWork_No_2 - EE 320 Homework No 2(Solution 1 A 0...

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