Expanding out PoS to SoP

Discussion in 'Homework Help' started by monkeyhead, Nov 12, 2008.

  1. monkeyhead

    Thread Starter Active Member

    Mar 5, 2007
    45
    0
    Hi there,


    I'm running through an exercise where I have to expand the PoS expression I've found and then expand it out so its factorised to leave the expression in a multi-level form.

    I've worked out my inital SoP expression is as follows:(note: / = not)

    /A . /D + /S . D + A.D

    I then used De morgans theorem to get:

    (/A + D) . (A + /S + /D)


    Expanded out I get:

    (A . /A) + (/A . /S) + (/A . /D) + (A . D) + (/S . D) + (/D . D)

    Which I've got to simplify too:

    (/A . /S) + (/A . /D) + (A . D) + (/S . D)

    then:

    /A (/S + /D) + D ( A + /S)

    I'm sure though that its supposed to be equivlanet to the initial expression but there seems to be an additional /S term which I cant get rid of!

    I'm not quite sure where I've gone wrong, so if someone would kindly point out where I've gone wrong that would be much appreciated!

    Kind regards,

    Matt


    :confused:
     
  2. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    monkeyhead,

    Lose that clunky, clumsy notation. Use instead A'B' + BC' + AB

    Expand out the above expression to get the minterms A'B'(C+C') + (A+A')BC' + AB(C+C') = A'B'C + A'B'C' + ABC' + A'BC' + ABC + ABC' .

    Discard one of the duplicate terms ABC' .

    Now, use a Karnaugh map or the Quine-McKCuskey method to reduce the expression to A'B' + AB + A'C' or equivalently A'B' + AB + BC'

    Ratch
     
    Last edited: Dec 27, 2009
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