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Design the logic circuit

  1. Jan 22, 2015 #1

    Zondrina

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    Homework Helper

    1. The problem statement, all variables and given/known data

    Draw the simplest logic gate or circuit for the description below. The inputs are ##a, b, c## and the output is ##z##.

    ##z = 0## only if ##abc = 010## or ##abc = 110##


    2. Relevant equations


    3. The attempt at a solution

    So i drew up a quick table, AND and OR'ed the required terms together and came up with this:

    IMG_0503.jpg

    Is this okay? The input ##a## seems to have disappeared, which makes no sense to me. Unless its some sort of trick question where I only need 2 inputs since the output doesn't rely on ##a## at all.
     
  2. jcsd
  3. Jan 22, 2015 #2

    berkeman

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    Staff: Mentor

    Have you tried checking your answer with a Karnaugh map? I get a different answer...
     
  4. Jan 22, 2015 #3

    berkeman

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    Also, have you tried plugging the two values back into your answer...?
     
  5. Jan 22, 2015 #4

    Zondrina

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    I'm trying to do this without a K-Map.

    Plugging the values of ##b## and ##c## into my answer does provide the correct output, but I am unsure about the input ##a##.

    I don't believe the answer is correct, and I am unsure how to algebraically simplify this if my above attempt is incorrect.
     
  6. Jan 22, 2015 #5

    berkeman

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    My apolgies! I missed in your OP that z=0 for those two terms. Your answer does look correct. Sorry for any confusion I caused...
     
  7. Jan 22, 2015 #6

    Zondrina

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    Thank you for the clear up. I was just slightly confused about the inputs, but the logic worked out that way I guess.
     
  8. Jan 22, 2015 #7

    NascentOxygen

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    You did well. An alternative is to write ##\bar z\ =\ \bar a b \bar c\ +\ ab\bar c##

    Then simplify this as you did with your expression earlier, to get z = ....

    The answers will be the same. :)
     
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