# simplify boolean expression

Discussion in 'Homework Help' started by Carebear516, Sep 12, 2011.

1. ### Carebear516 Thread Starter New Member

Sep 12, 2011
2
0
I would like to simplify the following:

x'y'z' + x'yz + xy'z +xyz'

Any help would be appreciated.

2. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
The All About Circuits forum has a policy to ask the members to try a bit on their own, posting their efforts, before receiving any help from the other members.

Please tell us what you have tried so far. Scan a piece of paper or type your approach.

3. ### Carebear516 Thread Starter New Member

Sep 12, 2011
2
0
I began with a timing diagram and was asked to find the simplest sum of products form. The above is as far as I could take it. Any hint on how to go further would be appreciated. I am simply stuck. I am pretty sure it can be further simplified. But, I don't see it.

Last edited: Sep 12, 2011
4. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
Have you been taught about Karnaugh maps? They are a very easy and visual method of simplify Boolean expressions. For the case at hand you need a 3-variable map.

If you put the minterms you found in a K-map, you will discover that this expression cannot be simplified further in a Sum of Products form. On the contrary it can be compacted a lot through the use of a XOR gate.