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Demorgan's Theorem Problem

  1. Jan 25, 2007 #1
    1. The problem statement, all variables and given/known data
    F = xy+x'y'+y'z

    Implement the boolean function using only And nad Inverter Gates.

    2. Relevant equations
    Demorgan's Theorem


    3. The attempt at a solution

    X' means inversion btw.

    So I thought how you do this is to invert the variables, and change the type of gate.

    Therefore, I had

    (xy)(xy)(yz')

    But if I actually use real numbers to check.. this conversion is wrong.

    Am I looking at the demorgan's theorem wrong? Please give me any suggestions
     
  2. jcsd
  3. Jan 25, 2007 #2
    Do you use xy to mean (x)(y) ?

    If so you forgot to apply ((x)(y))' = x' + y'

    If that doesn't make any sense it is because I made a bad guess at your notational conventions.
     
  4. Jan 25, 2007 #3
    I'm sorry, let me clarify a little bit.

    xy = x and y
    x+y = x or y
    (xy)(xy) = x and y anded with x and y
     
  5. Jan 25, 2007 #4
    I think you're looking at the theorem wrongly alright. Care to explain how F = xy+x'y'+y'z became F = (xy)(xy)(yz')?
     
  6. Jan 25, 2007 #5

    berkeman

    User Avatar

    Staff: Mentor



    Does this link help? (we've used it in a couple recent threads similar to yours):

    http://www.vias.org/feee/karnaugh_09.html
     
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