2

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.

kjhughes
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aSilveira
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2 Answers2

2

If i haven't made any mistakes it is pretty much the same, invert all 3 of the inputs and you get a NOR

Table:

AND with inverted in is exact the same as 

1 1 1 = 1           
1 1 1 = 0           
1 0 1 = 0           
0 1 0 = 0           
0 1 1 = 0           
0 1 0 = 0           
0 0 1 = 0           
0 0 0 = 0

NOR with original input

0 0 0 = 1            
0 0 1 = 0            
0 1 0 = 0            
1 0 1 = 0            
1 0 0 = 0            
1 0 1 = 0            
1 1 0 = 0            
1 1 1 = 0
JDurstberger
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  • By your logic I was able to understand this, thank you! Though I feel like there is something wrong with the input columns of your truth table. On the 4th row? – aSilveira Sep 25 '14 at 05:07
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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.

kjhughes
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