Question

Prove that the dual of the exclusive-OR gate is also itscomplement

Answer 1

Answer:

Explanation:

The dual of a function means replace AND with OR and replace OR with AND.

XOR gate of A , B is

$A \, XOR\, B = AB' + A'B$

So, Dual of A XOR B is ( replace AND with OR and OR with AND)

$= (A+B')(A'+B)$

Complement of A XOR B is $(A XOR B) ' = (AB' + A'B) ' = ((A)' + (B')') ((A')' + (B)') = (A'+B)(A+B')$ (In finding compliment AND becomes OR and OR becomes AND ).

By inter changing the above product of terms  

Complement of $A XOR B = (A + B') (A' + B)$

So, Dual of A XOR B = Complement of A XOR B.