[Digital Electronics] Gate 2011 ECE

Question

	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.

Comments

any means all.[anything ]

Answer 1

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..

Comments

Yes.I understand this point about regarding universal gate .But second statement is saying that it 

 It is not possible to realize any Boolean function using XOR gates only.

The counterexample for ANY is ,I realize one boolean function with exor gates.Say a 2 variable function wth minterms as(1,2),which is exor itself,and it can be realized.If it was as follow then i can say A option is correct.

 It is not possible to realize all Boolean function using XOR gates only.

Please let me know If i am getting this wrong

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I got it know after reading 3-4 times.:). Thanks

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Using Xor gate u can realize only buffer & not gate only.

other than this no implementation is possible like and,or gates using xor.