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Design a multiplexer circuit

  1. Jan 11, 2015 #1

    Zondrina

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    Homework Helper

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

    Design a multiplexer circuit given the data such that:

    When ##C = 0##, the output ##X = A##.
    When ##C = 1##, the output ##X = B##.

    The truth table is displayed below:

    Screen Shot 2015-01-11 at 10.18.34 AM.png

    2. Relevant equations


    3. The attempt at a solution

    I wanted to make sure I understood this and I wasn't overlooking anything.

    Looking at the ##A##, ##C## and ##P## columns, I deduced I needed a term of the form ##A \cdot \bar C##.

    Looking at the ##B##, ##C## and ##Q## columns, I deduced I needed a term of the form ##B \cdot C##.

    Looking at the ##P##, ##Q## and ##X## columns, I see I need a gate that satisfies ##\bar P \cdot Q + P \cdot \bar Q + P \cdot Q##.

    That last expression can be simplified to:

    ##\bar P \cdot Q + P \cdot \bar Q + P \cdot Q = \bar P \cdot Q + P(\bar Q + Q) = \bar P \cdot Q + P = Q + P##

    So from what I can gather, ##Q + P = B \cdot C + A \cdot \bar C##.

    Hence ##X = Q + P = B \cdot C + A \cdot \bar C##.

    Thank you.
     
  2. jcsd
  3. Jan 11, 2015 #2

    gneill

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    Staff: Mentor

    Looks okay. You might have considered using a Karnaugh Map approach which would yield the two terms by inspection.
     
  4. Jan 11, 2015 #3

    NascentOxygen

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    How did you fill in the P and Q columns?
     
  5. Jan 12, 2015 #4

    Zondrina

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    When ##C = 0##, the value of ##Q## does not matter and the value of ##X## depends only on ##A##.

    Similarly when ##C = 1##, the value of ##P## does not matter and the value of ##X## depends only on ##B##.

    This gives half a column of ##Q##s and ##P##s that do not matter. I could have filled those in with a ##d## or ##-##, but that was the problem statement provided and they seemed to have used a ##0##.
     
  6. Jan 14, 2015 #5

    NascentOxygen

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    Staff: Mentor

    This question is a bit puzzling. It's as though that table belongs to some other question and accidently got mixed in here.

    The task is wholly described in just these lines:

    Design a multiplexer circuit given the data such that:

    When C=0, the output X=A.
    When C=1, the output X=B.


    The table with signals P and Q is either a mistake or a red herring, IMO.
     
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