Expert: Zlatko - 7/20/2011

Question
How AND gate can be realized using NOR gate?"

Answer
You have 2 signals, A,B and you want A * B but you have only NOR gates.

A NOR B is !(A + B) where I am using ! to mean NOT
Using DeMorgan's rule A NOR B is !A * !B so the AND function can be emulated with NOR if you first invert the signals A, B. The NOR gate can be used as an inverter by tying the inputs together.
Therefore, to get the AND, you need 3 gates. Two to invert each input A,B, and one to NOR the inverted signals together.

Proof with truth table
A B !A !B (!A NOR !B)
0 0  1 1   0
0 1  1 0   0
1 0  0 1   0
1 1  0 0   1 <<- the only time the output is 1 is when both A and B are 1

See http://en.wikipedia.org/wiki/NOR_logic