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Karnaugh Map from Boolean Expression

  1. Mar 3, 2013 #1

    I'm trying to figure out a few questions on a practice exam that I'm working on for my Intro to Logic Systems class and could use some help.

    One of the questions (and the others are similar) says:

    Determine the minimized realization in the sum-of-produicts form using literals of the function:
    f(A,B,C) = [itex]\Sigma[/itex]m(4,6) + [itex]\Sigma[/itex]d(2,3,7)

    The given answer is f(A,B,C) = AC'.

    I know that [itex]\Sigma[/itex]m(4,6) can be represented by AB'C' + ABC' and that [itex]\Sigma[/itex]d(2,3,7) can be represented by A'BC' + A'BC + ABC, but beyond that I am not sure what to do. I think that I need to construct a Karnaugh map from the expression, but am not sure how to do it.

    Any help is greatly appreciated. Thanks!
  2. jcsd
  3. Mar 4, 2013 #2


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    Staff: Mentor

    Before embarking on a K-map, I suggest that you construct a truth table for your Boolean expression for f(A,B,C), and compare it with AC', to make sure you have that right.
  4. Mar 4, 2013 #3
    Thanks for the reply. I'm pretty sure that I know how to construct a Karnaugh map given a truth-table. But I do not know how to construct a truth-table given an expression like that. Can you help me with that?
  5. Mar 4, 2013 #4


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    Staff: Mentor

    Don't you just OR those two expressions:
    AB'C' + ABC' with A'BC' + A'BC + ABC?

    I assume that is the way to go.
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