How to derive XOR from only NOR gates

[Glavata]

Hi, Through some searching and guessing with LogiSim I was able to see how to build a XOR gate from only NOR gates. I would like to know what the process for deriving this would look like. Right now I am lost as to how to proceed given that the NOR function is A'B' and XOR is AB' + A'B. How would you get from only NOR gates to building a circuit equivalent to a 2 input XOR.

Thanks!

 

[dlgoff]

Welcome to PF.

See if this helps:

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

 

[zgozvrm]

I think this is what you're looking for:

AB' + A'B
= (0 + AB') + (A'B + 0)
= (AA' + AB') + (A'B + BB')
= A(A' + B') + B(A' + B')
= (A' + B')(A + B)
= (AB)'(A'B')'
= [(AB) + (A'B')]'
= [(A' + B')' + A'B']'
= [(A'A' + B'B')' + A'B']'
= ([(A + A)' + (B + B)']' + A'B')'
= ([(A + A)' + (B + B)']' + (A + B)')'

This formula represents your circuit: A NOR A is NOR'd with B NOR B. The result is NOR'd with A NOR B.