What is the difference between De Morgan's theorem and Principle of Duality?

@Kaustubh Katdare • 18 Jan, 2012 Never thought about this. Will have to look for Principle of Duality, will have to revise it once it before I post something useful. Can someone help in the mean time?

@nareshkumar6539 • 19 Jan, 2012

SheldonCooper

Can anyone tell me what is the difference between De Morgan's theorem and Principle of Duality?

Principle of Duality means (x,y,+,.,0,1)=>(x,y,.,+,1,0)to get a duality of an expression you need to convert + to . and viceversa ,0 to 1 and vice versa and varibles write as it is(varibles not complemented).If one gate follows some operation then its duality also follow the same operation.
Eg:Duality of OR operation is AND.OR follows commutative AND also follows the commutative.
Duality of NAND is NOR.
De Morgan's theorem it converts Universal realization into Basic realization and vice versa.
NAND-NAND(universal realization) to AND-OR(Basic realization) according to principle of duality
NOR-NOR(universal realization) to OR-AND(Basic realization)

@SheldonCooper • 21 Jan, 2012 What is the difference between X,Y and 0,1? Finally x and y will contain 1 and 0 won't they?
Consider following example-
X+Y=0 (OR gate so both X and Y should be 0)
now take the dual of it according to you
X.Y=1 (is it correct?)
But here to satisfy AND gate the values should be 1 and 1.That is X and Y got complemented values.
Now don't say you put x and y as it is (Symbols) but while putting their values you put them as complements.i.e.0 in place of 1 and vice versa.
Just explain it further.I have no intention of mocking you.😀

@SheldonCooper • 28 Jan, 2012 Is it the case that after applying De-Morgans theorem,the value of the function remains same.But after applying Principle of duality the value changes?
i.e.Dual of a function is not same as the original function but if De-Morgans theorem is applied on the original function then it is just another representation of the original function?

@Nick Naym • 08 Mar, 2012 • 1 like

SheldonCooper

Can anyone tell me what is the difference between De Morgan's theorem and Principle of Duality?

Duality is a metatheorem: If you prove a theorem, you've also proven its dual. De Morgan's Theorem is a tool for manipulating expressions.