Question

Show that the dual of exckusive OR is also its complement.

Answer 1

Exclusive OR

A Ex-OR B = A'B + AB'

Dual of a function: Change the OR to AND and OR to AND operation.

dual = (A'+B)(A+B')

compliment = (A'B+AB')'

(A'B)'(AB')'

(A+B')(A'+B)

which shows compliment and dual of EX-OR are equal.

Answer 2

A XOR B = A'B + AB'

(A XOR B)' = AB + A'B' ......(1)

In dual we replace AND with OR and OR with AND.

Dual of (A XOR B) = (A'+B) (A+B') = A'A +A'B' +AB+BB' = AB + A'B'..... (2)

from (1) and (2)

Dual of XOR = Complement of XOR