De-Morgan laws

[shahar]

Hello, I have a question. It isn't base on any document or written text.
I know we can exchange a set of electric components by another electric components to do the De-Morgan Law in Electric circuit.
Can I exchange the expression x'y' = x' + y' in electric circuit.
x and y are 1 or 0.

 

[Zermelo]

No you can’t. That would basically mean that a+b is the same as a*b (if we put a = x’, b = y’), which is nonsense. The DeMorgan laws are (x+y)’ + x’y’, and (xy)’ = x’ + y’. Try to think about what really happens in these circuits to understand this concept (draw them out, make a table that shows what happens for each combination of the values of x and y, look up “truth table” on the internet.)