4-1 to 2-1 Multiplexer Help

Discussion in 'Homework Help' started by vg19, Oct 18, 2006.

  1. vg19

    Thread Starter New Member

    Nov 3, 2004
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    I cannot seem to understand how in the attached diagram, they went from the 4-1 multiplexer to the 2-1 multiplexer.
    The main part is the modified truth table. I cant understand what is going on for the life of me!

    If someone could please explain this, it would be much apprecieated.

    Thanks!
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,145
    1,791
    They did not go from one implementation to the other. They are alternative ways of doing the same thing. If you draw a black box around the circuits and can only observe the inputs and the outputs then you cannot tell what is inside the box.

    The function which is implemented in both cases is called exclusive OR or XOR. In the first case inputs W1 and W2 select one of four constants to route to the output. In the second case W1 selects either W2 or its complement. As you can see the truth tables are identical.
     
  3. vg19

    Thread Starter New Member

    Nov 3, 2004
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    Hmmm I guess I just dont understand the second case. I dont understand how second case acts as the XOR...
     
  4. Papabravo

    Expert

    Feb 24, 2006
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    1,791
    W1 goes to the select input, W2 goes to the zero input, and W2-bar goes to the one input. If W1 == 0 the output is W2. If W1 == 1 then the output is the inverse of W2, W2-bar. This behavior is exactly the behavior of a two input exclusive OR gate and the 4:1 multiplexer. The truth table is right there next to the diagram, what's not to see and understand.
     
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