Boolean Algebra: Minimum Sum-Of-Products Expression

  1. 1. The problem statement, all variables and given/known data

    Find the minimum Sum-Of-Product Expression for:
    f = ab'c' + abd + ab'cd'

    3. The attempt at a solution

    By introducing the missing variable in term 1 and term 2 I can get an expression that has all the variables: a, b, c, and d.

    I do so by:

    f = ab'c'd + ab'c'd' + abcd + abc'd + ab'cd'

    I can combine terms like so: (1 & 2),( 2 & 5), (3 & 4) I get:

    f = ab'c' + ab'd' + abd

    This hardly seems minimized from the original expression. Thanks for any help.
    Last edited: Sep 13, 2009
  2. jcsd
  3. What you've stated is one of two equivalent minsum forms of that Boolean expression. There are several methods for arriving at these (consensus, Karaugh maps, Quine-McCluskey). I'd examine them for more info.

    The original expression has a summand complexity (SC) of 3 and a literal complexity (LC) of 10. The minsum has an SC of 3 and an LC of 9 (as does the other). It isn't much simpler but it as simple as one can get.

  4. Thanks, when you're learning about these concepts it is nice to have confirmation that you are doing things right. Normally it class we get the function down a term or two...or even to one term. So, when I got this down to three terms, with three variables in each term, it didn't really seem minimized. Thanks again!
  5. Karnaugh product of sums answer:

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