Need help simplifying boolean equation to SOP format

Discussion in 'Homework Help' started by redbuckeye84, May 12, 2008.

  1. redbuckeye84

    Thread Starter New Member

    May 12, 2008
    2
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    x= AB'(A'BC+DB)(BC+CD')+ABC+BC'D'+D(B'+C')

    ' = not......
    Any help would be appreciated. I've read over the proofs but am having trouble getting started.
     
  2. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    A good way to do it is to make a truth table according to your expression and then draw a Karnaugh map and simplify it.

    Is that ok or you need to do it by using boolean algebra?
     
  3. redbuckeye84

    Thread Starter New Member

    May 12, 2008
    2
    0
    Unfortunately I have to simplify it down by using boolean algebra.....
    How could i make a truth table by using that expression? I could take the results from the truth table then puts those in a k-map to pull the expression out. Which way is easier???
     
  4. hgmjr

    Moderator

    Jan 28, 2005
    9,030
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    Take a look at the material in the contained in the AAC ebook on the topic of boolean algebra.

    hgmjr
     
  5. mik3

    Senior Member

    Feb 4, 2008
    4,846
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    If you make the multiplications you get:

    (AB'A'BC+AB'DB)(AB'BC+AB'CD')+ABC+BC'D+DB'+DC'

    then AB'A'BC=0 , AB'DB=0 , AB'BC=0 because they have AA' and BB' in them

    and BC'D+DC'=D[BC'+C']=D[C'(B+1)]=DC'

    thus you get:

    AB'CD'+ABC+DB'+DC'

    i dont know if this is the simplest SOP but it is simplified

    if you want the simplest do it with Karnaugh map
     
    Last edited: May 13, 2008
  6. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    redbuckeye84,

    The first expression AB'(A'BC+DB)(BC+CD')=0 so all that is left is ABC+BC'D'+D(B'+C') mik3 made an error in reduction.

    Map it out on a 4 variable K-map and find out how the terms combine. Then chose the Boolean theorem that fits the groupings. The K-map also will find the correct answer or answers if there is more than one. Ask if you need more help. Ratch
     
    Last edited: May 13, 2008
  7. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    Ohh yes you are right :)

    But because he wants SOP the answer is ABC+DB'+DC'
     
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