# Minimisation of Boolean Functions

Theory
Algebraic
Manipulation of Boolean Expressions

Karnaugh
Maps

Tabular
Method of Minimisation

Exercises

### 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:

Algebraic
Manipulation of Boolean Expressions

Karnaugh
Maps

Tabular
Method of Minimisation

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*