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## Appendix D. Number Systems

Here are only numbers ratified.

William Shakespeare

Nature has some sort of arithmetic-geometrical coordinate system, because nature has all kinds of models. What we experience of nature is in models, and all of nature's models are so beautiful.

It struck me that nature's system must be a real beauty, because in chemistry we find that the associations are always in beautiful whole numbersthere are no fractions.

Richard Buckminster Fuller

OBJECTIVES

In this appendix you will learn:

• To understand basic number systems concepts, such as base, positional value and symbol value.

• To understand how to work with numbers represented in the binary, octal and hexadecimal number systems.

• To abbreviate binary numbers as octal numbers or hexadecimal numbers.

• To convert octal numbers and hexadecimal numbers to binary numbers.

• To convert back and forth between decimal numbers and their binary, octal and hexadecimal equivalents.

• To understand binary arithmetic and how negative binary numbers are represented using two's complement notation.

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Outline

D.1 Introduction

D.2 Abbreviating Binary Numbers as Octal and Hexadecimal Numbers

D.3 Converting Octal and Hexadecimal Numbers to Binary Numbers

D.4 Converting from Binary, Octal or Hexadecimal to Decimal

D.5 Converting from Decimal to Binary, Octal or Hexadecimal

D.6 Negative Binary Numbers: Two's Complement Notation

Summary

Terminology

Self-Review Exercises