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Makeing logic gate using only NAND Gates

  1. Sep 29, 2012 #1
    1. The problem statement, all variables and given/known data

    How to make a logic gates only using NAND gates of the following diagram.
    How many NAND gates I would have to use for that diagram


    2. Relevant equations



    3. The attempt at a solution
    I know that A bar bar + B bar bar =AB
    A bar bar B bar bar = A+B
    De-morgans Theorem
     

    Attached Files:

  2. jcsd
  3. Sep 30, 2012 #2

    CWatters

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    Does it? I would write...

    A.B = (A.B)'' = (A'+B')'

    so using your notation I make it..

    A.B = (A bar + B bar) bar

    As for the actual question... Remember you can make an inverter from a NAND gate.
     
  4. Sep 30, 2012 #3
    how many inverter I wud hve to use...little confusing I guess
     
  5. Oct 1, 2012 #4

    CWatters

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    Look at the top gate. It's an AND gate right, so what's the difference between an AND and a NAND? Compare the truth tables if necessary.

    As for the other gate...

    It's an OR gate (eg the OR/NOR family rather than the AND/NAND family) so that's a clue you will need to apply demorgan ..

    A+B
    which is the same as..
    = (A+B)''
    because Inverting twice has no effect. Then apply demorgan and see what you get.
     
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