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Exclusive Gates (XOR and XNOR)

XOR gate:

Laws: XOR holds commutative and associative law. 

1. A ⊕ B = B ⊕ A

2. (A ⊕ B) ⊕ C = A ⊕ (B ⊕ C)

i)  Enable input of XOR gate = 1 (acts as inverter)

ii) Disable input of XOR gate = 0 (acts as buffer)

Important point:

i) XOR gate is an odd number of 1’ detector, 

i.e. if the number of 1’s is odd ⇒ output = high

And if the number of 1’s is even ⇒ output = low

ii)  Performing XOR operation on A ‘n’ times,

Question:

What is the output of this circuit?

Solution:

Performing XOR operation on A 'n' times,

Here the number of XOR is even, and input is 1 for all.

So, the output is x.

XNOR Gate:

It holds commutative and associative

A ⊙ B = B ⊙ A

(A ⊙ B) ⊙ C = A ⊙ (B ⊙C)

i) Enable input of XNOR gate = 1 (acts as buffer)

ii) Disable input of XNOR gate = 0 (acts as inverter)

Important notes:

i) Performing  XNOR operation on A ‘n’ times, 

ii) If the number of inputs (n) is odd, XOR ≡ XNOR and if the number of inputs (n) is even, 

A ⊕ A ⊕ A = A ⊙ A ⊙ A  (odd number) and A⊕ A ⊕ A ⊕ A = A ⊙ A ⊙ A ⊙ A (even number).