C++ How to Program, Ninth Edition

D. Number Systems

Here are only numbers ratified.

—William Shakespeare

Objectives

In this appendix you’ll learn:

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

• To understand how to work with numbers 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.

Outline

D.1 Introduction

D.2 Abbreviating Binary Numbers as Octal and Hexadecimal Numbers ...