Simplification of Combinational Logic Circuits Using Boolean Algebra

Complex combinational logic circuits must be reduced without changing the function of the circuit.
Reduction of a logic circuit means the same logic function with fewer gates and/or inputs.
The first step to reducing a logic circuit is to write the Boolean Equation for the logic function.
The next step is to apply as many rules and laws as possible in order to decrease the number of terms and variables in the expression.
To apply the rules of Boolean Algebra it is often helpful to first remove any parentheses or brackets.
After removal of the parentheses, common terms or factors may be removed leaving terms that can be reduced by the rules of Boolean Algebra.
The final step is to draw the logic diagram for the reduced Boolean Expression.