De Morgan’s Theorems of Boolean Algebra [Digital Electronics]

In Digital ELectronics there are various laws and rules for the simplification of boolean functions which are basically used to minimize the complexity of digital hardware design by minimizing the boolean function.

“De Morgan’s Theorems of Laws” is one of the most powerful theorems used in digital electronics for the minimization of boolean function or equation either in the successive reduction method or in the K-Map method.

De Morgan’s theorems or Laws can be proved by the help of Complement laws. Let us prove De Morgan’s theorem with the help of the complement law od addition and complement law of multiplication.

Complement laws of addition state that if a variable (X) is added to its complement (X’) then the output will always be equal to ‘1’.

Similarly, the Complement laws of multiplication state that if a variable (X) is multiplied to its complement (X’) then the output will always be equal to ‘0’.

Let us prove both De Morgan’s Theorem :