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Convert the following expression to canonical Sum-of = Product form :(a) X + X’Y + X’Z’(b) YZ + X’Y |
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Answer» (a) X + X’Y + X’Y’ = X(Y + Y’)(Z + Z’) + X’Y(Z + Z’) + X’Z’(Y + Y’) = (XY + XY’)(Z + Z’) + X’YZ + X’YZ’ + X’YZ’ + X’Y’Z’ = Z(XY + XY’) + Z’(XY + XY’) + X’YZ + X’YZ’ + X’YZ’ + X’Y’Z’ = XYZ + XY’Z + XYZ’ + XY’Z’ + X’YZ + X’YZ’ + X’YZ’ + X’Y’Z’ By removing duplicate terms we get canonical Sum-of=Product form : XYZ + XY’Z + XYZ’ + XY’Z’ + X’YZ + X’YZ’ + X’Y’Z’ F = ∑(1, 2, 3, 4, 5, 6, 7) F = m1 + m2 + m3 + m4 + m5 + m6 + m7 (b) YZ + X’Y = YZ(X + X’) + X’Y(Z + Z’) = XYZ + X’YZ + X’YZ + X’YZ’ By removing duplicate terms we get canonical Sum-of=Product form : XYZ + X’YZ + X’YZ’ F = ∑(2, 3, 7) F= m2 + m3 + m7 |
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