conversion between SoP and PoS from K-map

Discussion in 'Homework Help' started by PG1995, Dec 10, 2011.

  1. PG1995

    Thread Starter Active Member

    Apr 15, 2011
    753
    5
    Hi

    Please have a look here to see my question about Morris Mano's book; this is MethodPOS from Floyd's book. Please help me with the question. Thanks a lot.

    Regards
    PG
     
  2. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    They say the same more or less. But before we start notice that in the Floyd page, the minimized POS expression is (A+B+C')(B'+C+D)(B+C+D'). The complements have slided off place.

    Okay, so the problem is to find the minimal PoS form. Mano says exactly what I have told you in a previous post. I think Floyd has a more intuitive approach. For example, look at the group in the K-map that is labeled (A+B+C'). In order to get that answer you must think that since that common values for these elements are A=0, B=0 and C=1, that corresponds to the group (A+B+C'). It is a bit of reverse thinking, that applies in the PoS form.

    In the end, the method is the same. Work with the 0s of the function and group them. What will you do after that is that differs between the two authors. Morris/Mano find the minterms of F' and complement them to get the maxterm factors, Floyd goes directly to expressing the PoS factors.

    Now, about you don't understand in the M/M solution: it's about a technique in the K-maps you haven't realized yet. Look here: http://www.allaboutcircuits.com/vol_4/chpt_8/6.html, where it says "Mapping the four p-terms above yields a group of four. Visualize the group of four by rolling up..."

    K-maps are toroidal, which means that their ends meet and wrap around. This property allows you to create groups in the 4-variable map like:
    {m0,m3,m8,m10}
    {m0,m4,m12,m8,m2,m6,m14,m10}
    {m1,m2,m9,m11}

    Is it more clear how M/M reach their solution?
     
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