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boolean-logicboolean-expressioncircuit

Boolean equation from circuit


Could someone please help me understand what the boolean equation performed by this circuit would be?

image


Solution

  • Label the output of the first mux X.

    Then, create a truth table for X, then Y:

    C D X A Y
    ---------
    0 0 1 0 1
    0 1 0 0 0
    1 0 0 0 0
    1 1 1 0 1
    0 0 1 1 1
    0 1 0 1 1
    1 0 0 1 1
    1 1 1 1 1
    

    From inspection of the truth table:

    Y = A + CD + C'D'