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Boolean Algebra

  1. Jun 15, 2010 #1
    1. The problem statement, all variables and given/known data

    F= A'C+A'B+AB'C+BC

    Express the function as sum of minterms, and find the ninimal sum of products.

    2. Relevant equations



    3. The attempt at a solution

    How do I do this? I really don't know. I know it is easy though. Any help is appreciated!
     
  2. jcsd
  3. Jun 16, 2010 #2
    If I had some function:

    f(a, b, c) = abc + abc'

    then we can perform these logical manipulations:

    f(a, b, c) = ab(c + c')

    Now, c can either be a 1 or a 0. If c is 1, then c' is 0, and if c is 0, c' is 1. Therefore, the OR of c and c' is always 1, because only one of the arguments needs to be a 1 for OR to return 1. So we can now simplify and write:

    f(a, b, c) = ab

    So how does this all relate to your first question? Well, you need to perform the reverse to backtrack to the canonical sum of products (sum of min terms). In my example, we'd say:

    f(a, b, c) = ab

    For every omitted variable, you'd multiply in (that variable + that variable') and then distribute:

    f(a, b, c) = ab = ab(c + c') = abc + abc'

    another example:

    f(a, b, c, d) = ab = ab(c + c')(d + d') = abcd + abcd' + abc'd + abc'd'

    And to answer the second part of your question, to arrive to a minimal sum of products, you need to do what i first described: find redundancies, undistribute, and eliminate them. Google k-map for a quick, visual approach to minimizing sums of products.
     
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