Principles of Modern Digital Design
Chapter One
Number Systems and Binary Codes
1.1 INTRODUCTION
In conventional arithmetic, a number system based on ten units (0 to 9) is used. However,
arithmetic and logic circuits used in computers and other digital systems operate with only
0's and 1's because it is very difficult to design circuits that require ten distinct states. The
number system with the basic symbols 0 and 1 is called binary. Although digital systems
use binary numbers for their internal operations, communication with the external world
has to be done in decimal systems. In order to simplify the communication, every decimal
number may be represented by a unique sequence of binary digits; this is known as binary
encoding. In this chapter we discuss number systems in general and the binary system in
particular. In addition, we consider the octal and hexadecimal number systems and fixed-and
floating-point representation of numbers. The chapter ends with a discussion on
weighted and nonweighted binary encoding of decimal digits.
1.2 DECIMAL NUMBERS
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