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Converting to just NANDs with DeMorgan's

  1. Oct 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Convert a3'a1 + a3'a2 + a3'a0 + a3a2'a1'a0'

    to an expression (well, it's a circuit eventually) that would only employ NAND and NOR gates. Use DeMorgan's Law.


    2. Relevant equations
    a'+b'=(ab)'

    3. The attempt at a solution
    I applied DeMorgan's as the problem suggested...

    (a3'a1)''+(a3'a2)''+(a3'a0)'' + (a3a2'a1'a0')''

    Which yielded:
    ( (a3'a1)' (a3'a2)' (a3'a0)' (a3a2'a1'a0')')'

    This is in just NAND and NOR gates, but the circuit isn't really aesthetically appealing... Is there a simplifying trick I'm missing? Or is this just what it is supposed to be?

    Thanks in advance!
     
  2. jcsd
  3. Oct 18, 2009 #2
    I would draw out the circuit first before doing any Boolean algebra using regular AND OR and INVERTER gates. Then when its all drawn, convert the AND and NOR gates to NAND and NOR. Put inverter circles on the inputs of the and OR gates to turn them into NANDs, and inverter circles on the output of the AND gates to turn them into NAND gates. Cancel out and redundant inverters. Should results in a full NAND-NAND realization of you circuit.
     
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