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Reduction of Boolean Expression to its Lowest From

  1. May 21, 2013 #1
    Hey Guys

    I am Currently doing my degree in information systems. At the moment the subject is PLC(Processing and Logic Concepts)

    I understand all of it, I am not sertain on how to start reducing a boolean expression. Once the first step is done I normally get it and can complete the process of reduction using the Laws.

    Does anyone know if i hint or a trick on where to start reducing a Boolean Expression

    EX. F = AB'C + ABC + A'B'C' + A'BC'

    I am not looking for the answer to the expression only a tip on how to start reducing these tipes of Expressions.

    Thank You in Advance
     
  2. jcsd
  3. May 21, 2013 #2

    HallsofIvy

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    I'm no expert on this but the first thing I would do is start looking for "similarities" in the terms. For example, I see both A and C in the first two, both A' and C' in the second two:

    F= AB'C+ ABC+ A'B'C'+ A'BC'= A(B+ B')C+ A'(B+ B')C'
    and, of course, those two now have the same "B+ B' " so is the same as
    F= (B+ B')(AC+ A'C')_

    You haven't said what you consider "reduced to its lowest form".
     
  4. May 21, 2013 #3
    HallsoIvy

    Thank You for your reply. It helped me alot. What I mean by Reduced to its lowest form is - The Boolean Expression is reduced to a point where no more Laws or Rules can be applied to the remainder of the original expression.

    Would I be correct if I reduced the expression from where you stopped to :

    F = (B+B')(AC+A'C')
    = (1)(AC+A'C')
    = AC + A'C'
    = AC

    Thank You for your help
     
  5. May 21, 2013 #4

    mathman

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    Stop at F = AC + A'C', you can't justify the last line.
     
  6. May 22, 2013 #5
    Thanks I see what you mean. I went to class last night and the same was said to me on how to start these expressions. Look for similarities, Thank You again for your assistance I am almost sure I got this now
     
  7. May 22, 2013 #6
    The last line can actually be done using an XNOR gate.

    BiP
     
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