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boolean-logiccircuit-diagram

How to convert a 3 input AND gate into a NOR gate?

I know that I can say convert a 2-input AND gate into a NOR gate by simply inverting the two inputs because of DeMorgan's Theorem.

But how would you do the equivalent on a 3-input AND gate?

Say...

     ____
A___|     \
B___|      )___ 
C___|____ /

I'm trying to understand this because my homework asks me to take a circuit and convert it using NOR synthesis to only use nor gates, and I know how to do it with 2 input gates, but the gate with 3 inputs is throwing me for a spin.

Solution

  • DeMorgan's theorem for 2-input AND would produce:

    AB
(AB)''
(A' + B')'

    So, yes, the inputs are inverted and fed into a NOR gate.

    DeMorgan's theorem for 3-input AND would similarly produce:

    ABC
(ABC)''
(A' + B' + C')'

    Which is, again, inputs inverted and fed into a (3-input) NOR gate:

         ___
A--O\    \
B--O )    )O--- 
C--O/___ /

    @SailorChibi has truth tables that show equivalence.