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

User Kiritsuku
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Answer:

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.

User Omkesh Sajjanwar
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