De Morgan Theorem and Demorgans LawsPublished on 24/2/2012 & updated on 25/8/2018
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There are actually two theorems that were put forward by De-Morgan. On the basis of DE Morgan’s laws much Boolean algebra are solved. Solving these types of algebra with De-Morgan's theorem has a major application in the field of digital electronics. De Morgan’s theorem can be stated as follows:-
Theorem 1: The compliment of the product of two variables is equal to the sum of the compliment of each variable. Thus according to De-Morgan's laws or De-Morgan's theorem if A and B are the two variables or Boolean numbers. Then accordingly
Theorem 2: The compliment of the sum of two variables is equal to the product of the compliment of each variable. Thus according to De Morgan’s theorem if A and B are the two variables then. De-Morgan's laws can also be implemented in Boolean algebra in the following steps:-
- While doing Boolean algebra at first replace the given operator. That is if (+) is there then replace it with (.) and if (.) is there then replace it with (+).
- Next compliment of each of the term is to be found.
De-Morgan's theorem can be proved by the simple induction method from the table given below.
Again different values of A and B we see the same thing i.e. column no 7 and 8 are equal to each other and 9 and 10 are equal to each other. Thus by this truth table we can prove De-Morgan's theorem. Some examples given below can make your idea clear. Therefore,
With the help of De-Morgan's theorem our calculation become much easier. Let other example be, In both the equations we have suitably used De-Morgan's laws to make our calculation much easier.
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