Can this Boolean Expression be simplified?

Discussion in 'Electronics & Electrics' started by Romen, Jan 29, 2014.

  1. Romen

    Romen Member

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    Helping someone out with this one....

    A'B'C'D'+A'B'CD+A'BC'D+A'BCD'+AB'C'D+ABC'D' = F

    Tried many times and not having much success with it.

    Any suggestions?


    Hope questions like this belongs in this forum!

    EDIT: ' means NOT and + means OR.
     
    Last edited: Jan 29, 2014
  2. heydonms

    heydonms Member

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    You're going to have to clarify your operators, I'm assuming ' means NOT and + means AND? ¬ and ^ the more traditional representations.

    If my understanding of your symbols is correct then maybe you should post the whole question because what you have there can be simplified to "X ^ ¬X = F" which is really just a description of the axioms you are working with.
     
  3. OP
    OP
    Romen

    Romen Member

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    Cheers.

    Sorry, ' means NOT and + means OR.
     
  4. Alby

    Alby Member

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    Yes it can :lol:
     
  5. heydonms

    heydonms Member

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    That makes sense I guess since there is obviously an implied AND between the operands. Next you will have to define what you mean by simplified. I see plenty of common factors that could be pulled outside of some brackets.
     
  6. OP
    OP
    Romen

    Romen Member

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    Smallest expression to cover it all and still get the outputs of:
    1
    0
    0
    1
    0
    1
    1
    0
    0
    1
    0
    0
    1
    0
    0
    0
     
  7. SLATYE

    SLATYE SLATYE, not SLAYTE

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    As above, you can pull out common factors if you want. However, nothing's going to cancel.
     
  8. OP
    OP
    Romen

    Romen Member

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    Cheers all.

    After sleeping on it came up with

    (A' OR C') AND (A XOR B) XOR (C XOR D)

    Was tired last night and didn't word the question correctly... My bad, sorry.

    Was meant to simplify the equation to use the least amount of gates possible.
     
  9. cvidler

    cvidler Member

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    I don't do boolean logic often enough to do it in my head easily, I find it helps to right out a result table. There's only four inputs, so you've got 16 maximum combinations.

    A B C D F
    0 0 0 0
    0 0 0 1
    0 0 1 0
    0 0 1 1
    etc.

    once you work out the result in each case, any patterns become obvious and you can then write a new equation to match the output.
     
  10. OP
    OP
    Romen

    Romen Member

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    Thge outputs were listed above.

    You end up with a k-map that looks like this:

    1 0 1 0
    0 1 0 1
    1 0 0 0
    0 1 0 0

    Worked out it can't be solved algebraically (well, you MIGHT be able to).
     

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