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Need to be sure of this boolean algebra problem's solution

  1. Nov 8, 2016 #1
    1. The problem statement, all variables and given/known data
    Express the function Y= (abd + c)' + ((acd)'+(b)')' as the complete disjunctive normal form:
    2.1 by applying Boole's theorerm,

    2. Relevant equations


    3. The attempt at a solution
    I separated the equations to two terms (T1,T2)

    T1= (abd + c)' T2=((acd)'+(b)')'

    T1= (abd+c)' T2=((acd)'+(b)')'
    =(abd)'.(c)' =(acd)".(b)''
    =((a)'+(b)'+(c)'+(d)'). (c)' = abcd
    = a'c'.(b+b') + b'c'(a+a') + c'd'(a+a')
    =a'c'(bd+(bd)')+b'c'(ad+a'd')+c'd'(ab+a'b')
    =a'c'bd+a'c'b'd'+b'c'ad+a'd'b'c'+abc'd'+a'b'c'd'


    T1+T2= a'bc'd+ab'c'd+abc'd'+abcd
     
  2. jcsd
  3. Nov 9, 2016 #2

    haruspex

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    Not sure how to interpret your working. I think you intended this as two columns of working, the left hand for T1 and the right hand for T2. In which case, your last steps in what I quoted above are
    =(abd)'.(c)' =((a)'+(b)'+(c)'+(d)')
    And
    =(acd)".(b)'' = abcd
    Neither of those are correct. Take them in smaller steps.
     
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