Consensus Theorem

Discussion in 'Homework Help' started by Darion026, Sep 21, 2011.

  1. Darion026

    Thread Starter New Member

    Sep 21, 2011
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    A'BD + AB'D' with the consensus theorem you are left with D + D' which equals 1 but what happens next? Do the D and D' just cancel and you add a 1 to the entire equation?

    Also for something like A'B + AB you get B + B which is just B so what happens? Do you just put B in one of the parts like A'B + A?

    I am a Freshman and just started an ece class and I am really lsot and confused with simplifying Boolean expressions. Any help is appreciated thanks!
     
  2. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    You might have got something wrong here. You can't factorize two terms using different variables from each one.
    A'BD+AB'D\neq D+D'\ and\\<br />
A'B+AB\neq B+B

    A correct factorization is
    A'BD+A'BD'=A'B(D+D')=A'B

    Read here for an example on the consensus theorem: http://en.wikipedia.org/wiki/Consensus_theorem
    I think key to the consensus theorem is the existence of three terms in a sum (or product) not two.
     
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