(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
