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Boolean Algebra Simplification Help

  1. Jan 31, 2012 #1
    1. The problem statement, all variables and given/known data
    A'B'C' + ABC' + A'BC + A'BC'.

    The ' denotes a bar over the previous letter.

    2. Relevant equations

    Simplification Rules

    3. The attempt at a solution

    C' (A'B' + AB) + A'B(C+C')

    C' (A'B' + AB) + A'B ..... or like so: A'B'C' + ABC' + A'B

    Is it possible to simplify the left expression any more? Does A'B' + AB = 1? When I did the K-map I got answers of

    A'C' + A'B + BC' (Although I am not entirely sure I did the K-map right because it came out like this.
    Code (Text):

    AB (00)   (01)    (11)    (10)
    c(0) 1....1.....1..........
     (1)  ........1.....................
    That is the K-map of the original equation. When getting the simplified answer using the K-map am I supposed to circle EACH group of two consecutive 1's? I will arrive at the answer I got when simplifying above (A'B'C' + ABC' + A'B) if I select the top left most 1's in a group, then a group of the middle 1 and bottom 1, and then the right most 1 all by itself. If I select them in a different way (left most top 2, then middle and bottom, then middle and top right) I will get the answer of (A'C' + A'B + BC').

    I am not sure which one is right and it is driving me crazy!

    I would appreciate any help guys! Thanks a LOT!

    The answer I arrived to also gives me the correct answer for the truth table, but it looks like it could be simplified to the above form. How do I go about doing that?

    Thanks for any help!
    Last edited by a moderator: Jan 31, 2012
  2. jcsd
  3. Jan 31, 2012 #2
    I THINK I figured it out, but I am not sure. I will pick up where I left off and leave it to you guys to tell me if I did it correctly.

    A'B'C' + ABC' + A'B=

    A'(B+B'C') + ABC' =

    A'(B+C') + ABC' =

    A'B + A'C' + ABC' =

    B(A' + AC') + A'C' =

    B(A' + C') + A'C' =

    A'B + BC' + A'C'

    This final answer is what I arrived to when I did the k-map. I am just not 100% sure if my methods for reaching the final answer is correct.

    Thanks for any help guys!
  4. Feb 3, 2012 #3


    User Avatar

    Staff: Mentor

    What you have in A'B is an INEQUALITY function--it evaluates TRUE iff A≠B
    What you see in blue is an EQUALITY function--it is TRUE iff A=B
  5. Feb 3, 2012 #4


    User Avatar

    Staff: Mentor

    There is no need to guess or hope. You can always draw up truth tables to show whether your simplification is right or not.
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