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[Digital Electronics] Gate 2011 ECE

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Assertion (A): XOR gate is not universal gate.

Reason (R): It is not possible to realize any Boolean function using XOR gates only.
A. Both A and R are correct and R is correct explanation of A
B. Both A and R are correct but R is not correct explanation of A
C. A is true, R is false
D. A is false, R is true

Answer Given is A.

How is R statement true.Exor gate is implementing a Exor,which is also one boolean function?If we say total functions on n variable is 2^2^n,then one of them is EXOR which will be implemented by EXOR.So should it be C?

I am specifically talking about "ANY" keyword in Second statement.

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But XOR is not able to realise all logic gates..We say a gate is universal gate if :

All logic functions possible in the given number of variables can be realised using that particular gate

e.g. if we take example of 2 variable functions , we can realise all of 16 functions using NAND gates or NOR gates only ..So NAND and NOR gates are also known as universal gates..

As for example OR using NAND : P ⋁  Q = (P ↑ Q)   ↑   (P ↑  Q)  

                             using NOR  :  P ⋁  Q  =  (P ↓ P)  ↓  (Q ↓ Q)  

Similarly we can realise other gates(boolean functions) using only NOR or only NAND gates hence they are referred as universal gates ..

As contrast to this , we can realise all functions using XOR functions only hence they are not considered as universal gates..

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