Introduction to Digital Electronics-Logic Minimization

Logic Minimization

              One thing you should know is that a digital logic circuit consists of a collection of logic gates, the input signals that drive them, and the output signals they produce.
The behavioral requirements of a logic circuit are best expressed through truth tables or logic equations, and any design problem that can be addressed with a logic circuit can be expressed in one of these forms. Both of these formalisms define the behavior of a logic circuit –how inputs are combined to drive outputs – but they do not specify how to build a circuit that meets these requirements.
            Minimisation of logic equation for a given logic system can be obtained by eliminating all non-essential or redundant inputs. The goal in “minimizing” logic systems is to find the simplest form by identifying and removing all redundant inputs.
Several methods have evolved to assist with the minimization process. Some of which are;
application of  Boolean Algebra
the use of Quine McCluskey Rule
use of searching algorithms.         
Although any of these methods can be employed using pen and paper, it is far easier (and more productive) to implement searching algorithms on a computer.