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' 2001, By Randall Hyde
Page
203
Intr
oduction to Digital Design
Chapter Three
Logic circuits are the basis for modern digital computer systems.
T
o appreciate how computer
systems operate you will need to understand digital logic and boolean algebra.
This chapter provides only a basic introduction to boolean algebra.
That subject alone is often
the subject of an entire textbook.
This chapter concentrates on those subjects that support other
chapters in this text.
Chapter Overview
Boolean logic forms the basis for computation in modern binary computer systems.
Y
ou can
represent any algorithm, or any electronic computer circuit, using a system of boolean equations.
This chapter provides a brief introduction to boolean algebra, truth tables, canonical representa

tion, of boolean functions, boolean function simplification, logic design, and combinatorial and
sequential circuits.
This material is especially important to those who want to design electronic circuits or write
software that controls electronic circuits. Even if you never plan to design hardware or write soft

ware than controls hardware, the introduction to boolean algebra this chapter provides is still
important since you can use such knowledge to optimize certain complex conditional expressions
within IF
,
WHILE, and other conditional statements.
The section on minimizing (optimizing) logic functions uses
V
eitch Diagrams
or
Karnaugh
Maps
.
The optimizing techniques this chapter uses reduce the number of
terms
in a boolean func

tion.
Y
ou should realize that many people consider this optimization technique obsolete because
reducing the number of terms in an equation is not as important as it once was.
This chapter uses
the mapping method as an example of boolean function optimization, not as a technique one
would regularly employ
. If you are interested in circuit design and optimization, you will need to
consult a text on logic design for better techniques.
3.1
Boolean Algebra
Boolean algebra is a deductive mathematical system closed over the values zero and one
(false and true).
A
binary operator
¡ defined over this set of values accepts a pair of boolean
inputs and produces a single boolean value. For example, the boolean
AND operator accepts two
boolean inputs and produces a single boolean output (the logical
AND of the two inputs).
For any given algebra system, there are some initial assumptions, or
postulates
, that the sys

tem follows.
Y
ou can deduce additional rules, theorems, and other properties of the system from
this basic set of postulates. Boolean algebra systems often employ the following postulates:
¥
¥
Closur
e
.
The boolean system is
closed
with respect to a binary operator if for every pair
of boolean values, it produces a boolean result. For example, logical
AND is closed in the
boolean system because it accepts only boolean operands and produces only boolean
results.
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 Summer '11
 JitenderKumarChhabra

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