Exclusive-OR (cont.)

Complement Law:

(X ? Y)’ = X ? Y’ = X’ ? Y

Algebraic Proof:

(X ? Y)’ = (XY’ + X’Y)’

= (XY’)’(X’Y)’

= (X’ + Y)(X + Y’)

= X’X + X’Y’ + XY + YY’

= 0 + X’Y’ + XY + 0

= X’ ? Y

= X’Y’ + XY

= XY + X’Y’

= X ? Y’

Previous slide

Next slide

Back to first slide

View graphic version