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Chapter: Digital Electronics - Minimization Techniques and Logic Gates

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De-Morgan’s Theorem

De Morgan suggested two theorems that form important part of Boolean algebra.

DE-MORGAN’S THEOREM:

 

De Morgan suggested two theorems that form important part of Boolean algebra. They are,



1) The complement of a product is equal to the sum of the complements.

 

(AB)' = A' + B'


 

•      FIRST THEOREM





2) The complement of a sum term is equal to the product of the complements.

 

(A + B)' = A'B'


•      SECOND THEOREM




 

APPLICATION OF DEMORGAN'S THEOREMS:

 

Apply to any number of variables:



 

PRINCIPLE OF DUALITY:

Principle of Duality theorem says,

·              Changing each OR sign to an AND sign

·              Changing each AND sign to an OR sign

·              Complementing any 0 or 1 appearing in the expression

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