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@SheldonCooper • 18 Jan, 2012 • 2 likes

Can anyone tell me 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

Duality of NAND is NOR.

NAND-NAND(universal realization) to AND-OR(Basic realization) according to principle of duality

NOR-NOR(universal realization) to OR-AND(Basic realization)

SheldonCooperCan 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.😀

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?

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

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

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