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Invert 3 signals using 2 NOT gates

Posted on: February 9th, 2016 by

You have 3 boolean inputs A, B and C. You want to obtain NOT(A), NOT(B) and NOT(C) all at once. However you are allowed to use at most 2 NOT gates. You may use as many AND and OR gates as you like. You may not use any other gates.

Can you build a circuit to achieve this?

- Via multiple sources including a bonus homework problem in school.

One Response to Invert 3 signals using 2 NOT gates

  1. Lizard had this to say about that:

    P123 = A or B or C
    P23 = (A and B) or (A and C) or (B and C)
    P3 = A and B and C

    P01 = not P23
    P1 = P01 and P123
    P02 = not (P1 or P3)
    P2 = P02 and P23
    P0 = P01 and P02

    NA = P0 or (P1 and (B or C)) or (P2 and B and C)
    NB = P0 or (P1 and (A or C)) or (P2 and A and C)
    NC = P0 or (P1 and (A or B)) or (P2 and A and B)

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