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Universal gate question

  1. Feb 18, 2015 #1
    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.

    1. The problem statement, all variables and given/known data

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

    2. Relevant equations


    3. 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.
     
    Last edited by a moderator: Feb 18, 2015
  2. jcsd
  3. Feb 18, 2015 #2

    lewando

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    Sorry, misread your post. Look into definitions or requirements of a universal gate.
     
    Last edited: Feb 18, 2015
  4. Feb 18, 2015 #3

    phinds

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    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?
     
  5. Feb 18, 2015 #4

    donpacino

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    Or prove that you can make a single NOR or NAND gate
     
  6. Feb 18, 2015 #5

    donpacino

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    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
     
  7. Feb 19, 2015 #6

    LCKurtz

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    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).
     
  8. May 11, 2015 #7
    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.
     
  9. Jan 20, 2016 #8
    Is it correct that AND and OR cannot be derived from XOR at all?
     
  10. Jan 20, 2016 #9

    phinds

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    what do you think, and why?
     
  11. Jan 20, 2016 #10
    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.
     
  12. Jan 20, 2016 #11

    phinds

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    I agree.
     
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