# Minimisation of Boolean Functions

Theory
Algebraic Manipulation of Boolean Expressions

Karnaugh Maps

Tabular Method of Minimisation

Exercises

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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.

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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*