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logicboolean-logic

Convert f(x1,x2,x3,x4) truth table to 4:1 multiplexer

How can I convert truth table of 4 variables into one 4:1 multiplexer

Here is an example how to convert it into 8:1 multiplexer

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Solution

  • The truth-table can in fact be implemented with a 2-1 multiplexer:

    enter image description here

    A minimized expression for the function depicted by the truth-table is

    Y = X1 X3 + X3' X4

    In words:
    Output Y is X1 for X3 true. For X3 false, Y is X4

    Input X3 selects either X1 or X4 to be forwarded to output Y.

    Input X2 is ignored (as don't care).

    You could use a 4-1 multiplexer and set the lower select input to X3, while the higher select input is set to constant 0.