# Reducing Boolean algebra

Discussion in 'Homework Help' started by cps13, Feb 25, 2013.

1. ### cps13 Thread Starter New Member

Feb 25, 2013
9
0
Hi,

I am new to the forum so hello to all.

I am studying a BTEC in EE and going onto a HND hopefully next year. I am struggling a bit with reducing boolean algebra. I seem to be able to look at the same problem 3 times and come up with three different answers.

Can someone give me some hints. If some is NOT for example NOT A I write it as A'

I have this problem.... ABC + A'B'C' + ABC' + A'C'

this is one way I have "solved" it.

ABC + A'B'C' + ABC' + A'C'
ABC + A'B'C' + ABC' + A' . 1 (last C' cancelled against first C, turns into 1 (A+A' = 1))
AB + A'B'C' + C' + A' . 1 (cancelled first AB against second AB in third group)
AB + A'B'C' + A' . 1 (cancelled second C' as same as C' in second group)
AB + B'C' + A' . 1 (A' in second group removed as same as last A')
AB + B'C' + A' (A' . 1 = A')

Any help would be greatly appreciated!

Thanks!

2. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
I don't think you are allowed to do the 1st step of your logic.

Consider this sentence: F=ABC+A'C'
for C=1, F=AB
for C=0, F=A'

Now, if according to your reasoning I write F=ABC+A' then
for C=1, F=AB+A'
for C=0, F=A'

These two expressions aren't the same.

Make another effort. Look up in your textbook for the available Boolean identities.

3. ### cps13 Thread Starter New Member

Feb 25, 2013
9
0
Changing that method I come up with ABC + A'B'C'

Am I any closer?

4. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
One of the nice things about problems like this (and a surprisingly high fraction of problems in engineering in general), is that you can check the validity of your answer from the anwer itself.

In this case, you have the given function:

F = ABC + A'B'C' + ABC' + A'C'

You have "simplified" it (whatever that means) and come up with:

G = ABC + A'B'C'

Both represents functions with a total of eight possible input conditions, so the truth table for each is very tame. Write out the truth tables for each. If they match, the functions are equal, if they don't, they aren't. Figuring out how to get to G may or may not be tricky, but determining whether G is a valid answer is trivial and should ALWAYS be done whenever practical.

Look for pairs of terms that have common factors, expecially if the only differ in one term.

Dec 2, 2008
3
0
ABC+A'B'C'+ABC'+A'C' =

AB(C+C')+A'C'(B'+1) =

C+C' = 1 and B'+1 = 1 so the equation will reduce to

AB+A'C'

6. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
It was kind of you to provide a full solution, but for the threads in the Homework Help section, we prefer to offer hints and help for the inquirer to reach the final result by his own means. It is more educational that way.