Proving XOR Gate Universality: Elementary Operations & Logical Manipulation

[braceman]

Hi guys, got a question that's got me stumped. Not looking for the answer as I'd prefer to work it out myself, just a nudge or a pointer in the right direction.
I'm being asked to prove if an XOR gate can be classed as universal (like the NAND & NOR gates are), but not sure how to go about it. I think there must be a simple way to do it, rather than draw numerous combinations of XOR gates.

Homework Statement

Determine the elementary operations that can be derived from XOR and hence determine if it is a universal gate.

Homework Equations

The Attempt at a Solution

Obviously got the truth table for XOR, am I supposed to be manipulating this, or taking a function, ie - F = A.B + C. not A and then trying to manipulate this like we do when converting to NAND/NOR (changing gates and inverting terms etc).

Bit stuck, so any pointers would be grateful.

 

[lewando]

Sorry, misread your post. Look into definitions or requirements of a universal gate.

 

[phinds]

To prove that gate type X is "universal", you just need to show that the Boolean functions AND, OR, and NOT can be implemented using only gate type X without the need for any other type gate. Can you do that with an XOR gate?

 

[donpacino]

To prove that gate type X is "universal", you just need to show that the Boolean functions AND, OR, and NOT can be implemented using only gate type X without the need for any other type gate. Can you do that with an XOR gate?

Or prove that you can make a single NOR or NAND gate

 

[donpacino]

here is a hint. first see if you can make an inverter
then see if you can make any input a 'blocker.' an example of that is an and gate, if any input is a zero, the ouput will be zero, independent of any other input

 

[LCKurtz]

Here's another hint: Try to prove you can't make an AND gate. (I don't think this is so easy to show if you haven't seen an argument before though).

 

[braceman]

Sorry I haven't posted back...forgot all about this post. I got it right in the end, Instructor said I could prove it however I wanted, so I just drew various combinations of 3-4 gates and their associated logic.

 

[bizuputyi]

Is it correct that AND and OR cannot be derived from XOR at all?

 

[phinds]

Is it correct that AND and OR cannot be derived from XOR at all?

what do you think, and why?

 

[bizuputyi]

What I meant is that an AND or OR gated cannot be derived by using only XOR gates. We can however make an inverter out of a XOR gate by connecting constant high to one of its input but I can't see any possible way to get either AND or OR from only XORs. To account for that I would say XOR gives high output only if its two inputs differ.

 

[phinds]

What I meant is that an AND or OR gated cannot be derived by using only XOR gates. We can however make an inverter out of a XOR gate by connecting constant high to one of its input but I can't see any possible way to get either AND or OR from only XORs. To account for that I would say XOR gives high output only if its two inputs differ.

I agree.