Page 53 - Handout Digital Electronics

LECTURE 7 MINIMIZING BOOLEAN FUNCTIONS

7.1 Introduction
Minimizing a Boolean function simply means simplifying it. There are several reasons for minimizing
Booleans functions. Booleans functions are used to implement logic gates or digital logic circuits, so a
simple Boolean function will use a smaller number of logic gates, and this will in turn offer the
following benefits to the designers:
• The Boolean function becomes easy to understand and implement
• When minimized, the function is less prone to errors and in its interpretation
• Minimized Boolean functions reduce the cost of implementation
• They reduce propagation delays in the circuits and improve circuit performance
• Power consumption is also reduced.

Consider the Boolean function:

F = A + AB . The digital logic circuit of this Boolean function is shown below:

This Boolean function minimizes F = A which is a Buffer

It is clear from the above that a minimized Boolean function has many advantages compared to a
complex Boolean function. Minimization can be achieved by several methods; four well-known
methods are:

• Algebraic method of minimizing Boolean Functions/Expressions
• Karnaugh Maps
• Tabular Method of Minimization
• Tree reduction
This module is limited to the algebraic, Karnaugh maps and the tabular methods.

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