DIGITAL DESIGN

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
DO NOT
COPY
DO NOT
COPY
DDO
NOT
COPY
DO NOT
COPY
DO NOT
Number Systems and Codes
Copyright © 1999 by John F. Wakerly Copying Prohibited
2
c h a p t e r
igital systems are built from circuits that process binary digits—
0s and 1s—yet very few real-life problems are based on binary
numbers or any numbers at all. Therefore, a digital system
designer must establish some correspondence between the binary
digits processed by digital circuits and real-life numbers,
events, and conditions. The purpose of this chapter is to show you how
familiar numeric quantities can be represented and manipulated in a digital
system, and how nonnumeric data, events, and conditions also can be
represented.
The first nine sections describe binary number systems and show how
addition, subtraction, multiplication, and division are performed in these
systems. Sections 2.10–2.13 show how other things, such as decimal numbers,
text characters, mechanical positions, and arbitrary conditions, can be
encoded using strings of binary digits.
Section 2.14 introduces “n-cubes,” which provide a way to visualize
the relationship between different bit strings. The n-cubes are especially
useful in the study of error-detecting codes in Section 2.15. We conclude the
chapter with an introduction to codes for transmitting and storing data one
bit at a time.
21