Electrical Engineering ⇒ Topic : De Morgans Theorems

De Morgan's Theorems

De Morgan proposed two important theorems which form a vital part of Boolean algebra. The two theorems in the equation form are given below:

(i) AB = A + B

i.e., the complement of a product is equal to the sum of the complements. Figure (a) illustrates this theorem.

                                           figure (a) De Morgan's theorem

Table (b) gives the truth table of this theorem.

                                             Table (b) Truth table of AB = A+ B

(ii) A+B=AB

i.e., the complement of a sum is equal to the product of the complements. Figure (c) illustrates this theorem and Table (d) gives the truth table of this theorem.

                                     Figure (c) De Morgan's theorem

Table (d) gives the truth table of this theorem.

Table (d) Truth table of A+ B = A . B

Table (e) summarizes the basic rules which are useful in manipulating and simplifying Boolean algebra expressions

                                                             Table (e) Basic rules