文档介绍：Number Systems
The concept of number is the obvious distinction between beast and man. Thanks to number, the cry
es song, noise acquires rhythm, the spring is transformed into a dance, force es dynamic, and
outlines figure.
-Joseph De Maistre
Introduction
In this appendix, we briefly review the concept of positional number systems, the methods for
conversion between alternative number systems, and the basic elements of binary addition and
subtraction. If you are not familiar with these concepts, it is probably a good idea to read this appendix
before starting out with Chapter 1.
Throughout much of our lives, we have been exposed to the base 10 number system. The preference for
10-digit number systems is no surprise: we have 10 fingers! However, this is not natural for digital
hardware systems, where arithmetic is based on the binary digits 0 and 1. We will also discuss number
systems that are variations on the binary system: octal (the digits 0 through 7) and hexadecimal. The
latter is a base 16 system, with 0 through 9 extended by the additional digits A (10), B (11), C (12),
D (13), E (14), and F (15).
Table of Contents
1. Positional Number Notation
2. Conversion Between Binary, Octal, and Hexadecimal Systems
3. Binary Arithmetic Operations
Appendix Review
Exercises
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Positional Number Notation
In this section, we cover the main positional number systems used in digital hardware: decimal, binary,
octal, and hexadecimal.
Decimal Numbers
The decimal number system represents quantities using the digits 0 through 9, arranged in a positional
notation. For example, in base 10, the number 154 can be represented as
This is called positional because a digit's "place" in the sequence determines its weight. The least
significant digit, in the rightmost position, has a weight of 1. The next digit to the