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Homework Help: Boolean logic expansion issue (POS -> CPOS)

  1. May 27, 2014 #1
    1. The problem statement, all variables and given/known data
    Convert f=(x'+y)(x+z)(y+z) from product of sums form, into the canonical product of sums.

    2. Relevant equations
    boolean logic, et al.

    3. The attempt at a solution

    This is boolean logic (so + is "or" and * is "and" etc..)

    There has to be some stupidly simple thing I am overlooking here. I chose to break it down and work each Maxterm by itself.

    So the first thing to expand is:
    and so:
    (x'+y) = x' + y + zz' since zz' = 0 this is okay.

    Now here is the part I am not following.

    I know that x' + y + zz' = (x' + y + z)(x' + y + z')

    but I don't know how this expansion is happening.
  2. jcsd
  3. May 27, 2014 #2


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    Homework Helper

    This is just the distribution rule: ##A \cup (B \cap C) = (A \cup B) \cap (A \cup C)##.

    PS. Learn the rules by heart, there aren't too many of them.
  4. May 27, 2014 #3
    oh god your right.


    I should have just wrote it out without all the + and * nonsense and I would have seen that.
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