Question

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

Answer 1

Step-by-step 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.