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zysi [14]
3 years ago
10

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

Computers and Technology
1 answer:
Tresset [83]3 years ago
7 0

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.

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