simplify boolean expression

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

  1. Carebear516

    Thread Starter New Member

    Sep 12, 2011
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    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
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    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
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    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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