# Boolean Simplification

Discussion in 'General Electronics Chat' started by MWalden, Jun 4, 2007.

1. ### MWalden Thread Starter Member

Apr 26, 2007
22
0
First I want to say whoever wrote the E-Book volumes on this website did a very good job. They make it very easy to understand. I am reading the Digital section. But it's missing one thing, maybe some tests or quizes written in javascript to help practice especially in the digital section. I'd be willing to help I can write a little in javascript and html. Just an idea.

Does anyone know where I can get some practice in Boolean simplification or any type of digital work, like tests/quizes/practice problems?

But anyway I have a question. To practice on the simplification I tried to simplify a simple adder circuit I got from HSW http://computer.howstuffworks.com/boolean2.htm They show a simple adder circuit but then say that it isn't the best way to do it that it can be done with fewer gates, so I have been trying to simplify it. Could someone tell me if I am doing this right or what:

First I converted it into an equation...
For Q:
(AB'+A'B)C' + (AB+A'B')C =
AB'C'+A'BC'+ABC+A'B'C
Since there are 3 variables grouped together I can't figure out how to simplify it any further than it already is? Am I doing something wrong?

The (AB'+A'B) is the XOR gate of course. The (AB+A'B') is the XNOR gate correct? (Which I got like this:
(AB'+A'B)' = (AB')'(A'B)' = (A'+B)(A+B') = AA'+A'B'+AB+BB' = A'B' + AB ? with DeMorgans theorem)

For CO (Carry out):
(AB)C'+(A+B)C =
ABC'+AC+BC =
A(C+C'B)+BC =
A(C+B)+BC OR AB+AC+BC

I got this one down a little, but can it go any further and am I doing it right?

Sorry if this is the wrong section of the forum.
Thanks for any help.

2. ### Dave Retired Moderator

Nov 17, 2003
6,960
145
Try our sister project the Socratic Project: http://www.ibiblio.org/kuphaldt/socratic/doc/topical.html

No. Assuming you have the compliments available, this expression requires only 5 gates. I can't see a way to simply this more.

Correct.

Your simplification looks fine here. You have options for your final expression, but would recommend you leave it in the form of A(C+B)+BC

Dave

3. ### MWalden Thread Starter Member

Apr 26, 2007
22
0
Cool! Thanks for your help and the website!