# Consensus Theorem

#### Darion026

Joined Sep 21, 2011
1
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!

#### Georacer

Joined Nov 25, 2009
5,182
You might have got something wrong here. You can't factorize two terms using different variables from each one.
$$A'BD+AB'D\neq D+D'\ and\\ A'B+AB\neq B+B$$

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.