Lec-5/logic/ Simplifications and minimization of Boolean function

Simplification And Minimization Of Boolean Functions

1. Simplification Of Boolean Expressions Using Algebraic
When a Boolean expression is implemented with logic gates, each literal in the function is designated as input to the gate.
Minimization of the number of literals and the number of terms leads to less complex circuits as well as less number of gates, which should be a designer’s aim.

There are several methods to minimize the Boolean function. Here, simplification or minimization of complex algebraic expressions will be shown with the help of postulates and theorems of Boolean algebra. This minimization procedure is not unique because it lacks specific rules to predict the succeeding step in the manipulative process.
Example 1. Simplify the Boolean function F=AB+ BC + B?C.
Solution. F = AB + BC + B?C
= AB + C(B + B?)
= AB + C
Example 2. Simplify the Boolean function F= A + A?B.
Solution. F = A+ A?B
= (A + A?) (A + B)
= A + B