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Boolean Algebra Simplification

  1. Aug 27, 2012 #1
    1. The problem statement, all variables and given/known data

    Simplify the following boolean expression:

    A'C + A'C'D + ABC + ABC'D

    I have a solution but when I checked against a boolean algebra simplifier online it gave me a different answer... is there a glaring mistake below ?

    2. Relevant equations

    None.

    3. The attempt at a solution

    A'C + A'C'D + ABC + ABC'D
    = A'(C + C'D) + AB(C + C'D)

    = A'(C + D) + AB(C + D) = A'C + A'D + ABC + ABD

    = C(A' + AB) + D(A' + AB)
    = C(A'B + 1) + D(A'B + 1)

    = C(1) + D(1) = C + D.

    Any help would be much appreciated !
     
  2. jcsd
  3. Aug 27, 2012 #2

    gabbagabbahey

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    This isn't correct. Consider that if [itex]A[/itex] is true and [itex]B[/itex] is false, then [itex]A' + AB[/itex] is false, while [itex]A'B + 1[/itex] is always true.
     
  4. Aug 27, 2012 #3

    rude man

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    You did so well with (C + C'D) = (C + D) at the start; use the same deal here.
     
  5. Aug 28, 2012 #4
    Hmm right so I could say that (A' + AB) = (A' + B)

    In which case C(A' + B) + D(A'+B) = A'C + BC + A'D + BD.

    I'm a little stumped as to how this simplifies further.

    Any help would be much appreciated !

    Sorry the answer should be BC + BD + A'C'D !
     
    Last edited: Aug 28, 2012
  6. Aug 28, 2012 #5

    gabbagabbahey

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    I think the answer you have in front of you is wrong. I get the same thing as you, which can be rewritten as (A'+B)(C+D). Wolfram Alpha also agrees.
     
  7. Aug 28, 2012 #6
    Great, thanks so much !
     
  8. Aug 28, 2012 #7

    gabbagabbahey

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    You're welcome!:smile:

    P.S. To see why BC + BD + A'C'D is incorrect, consider the case where A is false and C is true. To see why BC + BD + A'B' is incorrect, consider the case where both A and C are false.
     
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