# hw1_sol - ECE/CS 3700 Solutions to HW 1 Problem 1 a(X Y(X Y...

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ECE/CS 3700 Solutions to HW 1 Problem 1: a) (X+Y)(X+Y’) = XX + XY’ + XY + YY’ = X + XY’ +XY + 0 = X(1 + Y’ + Y) = X(1 + Y’ + Y) = X(1 + 1) = X b) X(X + Y) = XX + XY = X(1 + Y) = X(1) = X c) X(X + Y’) = XX + XY’ = X(1 + Y’) = X(1) = X d) (X + Y)(X’ + Z) = XX’ + XZ + YX’ + YZ = XZ + YX’ + YZ(X + X’) = XZ + YX’ + XYZ + X’YZ = XZ + XYZ + YX’ + X’YZ = XZ(1 + Y) + YX’(1 + Z) = XZ + YX’ MULTIPLEXER FUNCTION e) XYZ + XY' = X(YZ +Y') = X(YZ + Y'(Z+Z')) = X(YZ + Y'Z + Y'Z') = X(YZ + Y'Z + Y'Z +Y'Z') DUPLICATE Y'Z = X(Z + Y') = XZ + XY' Problem 2: a) (x + y)(x’ + y)(x + y’)(x’ + y’) = (x + y)(x’ + y’)(x’ + y)(x + y’) = (xx’ + xy’ + yx’ + yy’)(x’x + x’y’ + yx + yy’) = (xy’ + yx’)(x’y’ + yx) = xy’x’y’ + xy’yx + yx’x’y’ + yx’yx = 0y’ + 0x + 0x’ + 0y = 0

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b) x’(y’ + z’)(x + y + z’) = (x’y’ + x’z’)(x + y + z’)
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hw1_sol - ECE/CS 3700 Solutions to HW 1 Problem 1 a(X Y(X Y...

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