# Minimisation of Boolean Functions

Theory

### Theory: What is minimisation?

In mathematics expressions are simplified for a number of reasons, for instance simpler expression are easier to understand and easier to write down, they are also less prone to error in interpretation but, most importantly, simplified expressions are usually more efficient and effective when implemented in practice.

A Boolean expression is composed of variables and terms. The simplification of Boolean expressions can lead to more effective computer programs, algorithms and circuits.

Before continuing with this section, you should make sure you are familiar with the following topics:

Minimisation can be achieved by a number of methods, four well known methods are:

Tree reduction

Bear in mind that the Tree reduction method will not be looked at in this tutorial.

### Exercises

Using the tabular minimisation LabVIEW simulation, minimise the following:

Z = f(A,B,C,D) = AB + BCD + ABC

Z = f(A,B,C,D) = + AD + B

Z = f(A,B,C,D) = ABD + CD + ABCD

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Composed by David Belton - April 98