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Boolean Expression to 2-input logic gates only

Discussion in 'Electronics Homework Help' started by power13, Oct 28, 2018.

  1. power13

    power13

    9
    0
    Oct 26, 2018
    Hello,

    I have a Boolean expression and I want to convert it to circuit with only 2-input gates and NOTs.

    x'y'z + x'yz' + xy'k' + xyk

    Is there any different approach than:

    (x'y')z + (x'y)z' + (xy')k' + (xy)k



    Thought like this:
    and3.png
     

    Attached Files:

  2. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

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    Jan 21, 2010
    You could also try using de Morgan's theorem and see if it simplifies anything.

    Alternately, just implement a three input gate with two two input gates and invert the inputs as required.

    Have you created a truth table for it?
     
  3. power13

    power13

    9
    0
    Oct 26, 2018
    My expression is simplified by Karnaugh map.

    Unfortunately I think de Morgan's theorem doesn't helps here.
     
  4. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

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    Excellent. What did you come up with?
     
  5. power13

    power13

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    0
    Oct 26, 2018
    The result of K-map is this expression:

    x'y'z + x'yz' + xy'k' + xyk

    And now I want to draw the circuit with only 2input logic gates and NOTs.
     
  6. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

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    Jan 21, 2010
    Aaah! I thought that was what you had modeled in the K-map.

    Why not start with something like this:

    x'y'z + x'yz' + xy'k' + xyk
    x'(y'z + yz') + x(y'k' + yk)
     
  7. power13

    power13

    9
    0
    Oct 26, 2018
    Thank you for your help.

    After some reading of Boolean Algebra, I ended up with this expression:

    ( (NOT X) AND (Y XOR Z) ) OR ( X AND (NOT (Y XOR K)) )

    I think it is a good expression with 2 xor, 2 and, 2 not's.
     
  8. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

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    Jan 21, 2010
    Just be aware that a 2 input XOR gate may not be an allowable gate. Check this out, if you can.
     
    power13 likes this.
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