Boolean Algebra: Consensus theorem trouble.

Discussion in 'Homework Help' started by Mckayman, Sep 7, 2009.

  1. Mckayman

    Thread Starter Active Member

    Jun 22, 2009
    I have a few homework problems that are really troubling me in my logic's course. On these I really don't even understand were too begin. These problems are in regard to the consenses theorem.

    The problem calls for simplifying each the following expressions using only the consensus theorem (or its dual):

    a)BC'D' + ABC' + AC'D + AB'D + A'BD' (reduce to three terms)

    b)A'BC' + BC'D' + A'CD + B'CD + A'BD

    c)(B + C + D)(A + B + C)(A' + C + D)(B' + C' + D')

    And info or ideas would greatly be appreciated.


  2. Ratch

    New Member

    Mar 20, 2007

    I will do the first one for you, then you can do the rest.

    [A'BD'+ABC'+BC'D']+[ABC'+AB'D+AC'D] Rearrange and add another ABC' term
    [A'(BD')+A(BC')+(BD')(BC')]+[(AC')B+(AD)B'+(AC')(AD)] Group concensus
    A'BD'+ABC'+ABC'+AB'D Drop duplicate term

    So how did I know how to rearrange the terms and add a duplicate term? The answer is that I used a Karnaugh map to see what the concensus terms were. Then it was easy to group them and apply the theorem. Of course, you don't have to show your Karnaugh map, do you? People will think you are a genius at seeing those consensus patterns if they don't know about K-maps. You can spend a lot of time trying to find the pattern without the K-map.

  3. Mckayman

    Thread Starter Active Member

    Jun 22, 2009
    Thanks for your reply.