simplify boolean expression

Thread Starter

Carebear516

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

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

Any help would be appreciated.
 

Georacer

Joined Nov 25, 2009
5,154
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.
 

Thread Starter

Carebear516

Joined Sep 12, 2011
2
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:

Georacer

Joined Nov 25, 2009
5,154
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.
 
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