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Boolean Algebra Reduction

  1. Jan 15, 2007 #1
    I just started Digital Systems coursework and it seems our professor felt like giving us a book that has no examples and progresses the class with no examples as well. So basically we are stuck trying to learn Boolean algebra reduction with no real guidence.


    Anyways, I'm looking for some help:

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

    (x'y'+z')' +z +xy+ wz

    2. The attempt at a solution

    all I can see is this:

    (x'y'+z')' +z +xy
  2. jcsd
  3. Jan 15, 2007 #2


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    Staff: Mentor

  4. Jan 15, 2007 #3
    Sorry, I'm having a very difficult day (IE trying to do all my homework and NONE of it, it seems, I can accomplish, either to my shoddy math skills or lack of guidence).


    I really just need how to deal with that first expression:


    There isn't an example in the book and the one example in the lecture notes doesn't include any sort of situaion. I have been trying to guess at it:

    [(z+x')(z+y')]'+z +xy
    (z+x') + (z+y')+z +xy
    z +x' + y'+xy

    The book says I should get x + y + z as my answer, but I don't see it. I assume we will learn those maps next since it's in the book, but I'm pretty sure this is the type of prof that wants it done his way and when he says it.
  5. Jan 15, 2007 #4


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    Staff: Mentor

    To work on (x'y'+z')', use DeMorgan's Laws:


    first expand the x'y' term (express it as an OR of two terms), and then apply the appropriate DeMorgan's Law to take the NOT of the whole expression.
  6. Jan 16, 2007 #5
    (x'y'+z')' +z +xy+ wz
    = use de morgan's law, (x.y)' = x' + y' | (x+y)' = x'.y'
    = take out the common factor, anything +1 = 1
    = z.1 + xy
    = z + xy

    hope this helps
    Last edited: Jan 16, 2007
  7. Jan 16, 2007 #6


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    Staff: Mentor

    I'm going to leave this solution for now because I think Bob has worked it out by now. I'm going to issue chickens a 0-point warning for posting a complete solution to a homework problem, however.
  8. Jan 16, 2007 #7
    didnt know i can't do that, really sorry, next time will post a guided solution rather than a complete one
  9. Jan 16, 2007 #8


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    Staff: Mentor

    No worries. The PF is a special place. I have a feeling that you'll fit in well here.
  10. Mar 15, 2007 #9
    hi you can use one very good programs for that .
    Karnaugh Analyzer

    with that program you can get even the circuit. :surprised
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