Chapter 3. Data Representation

Table of Contents

3.1. Motivation
3.2. Orders of Magnitude
3.3. Numeric Limitations of Computers
3.4. Fixed Point Number Systems
3.5. Binary Data Representation
3.6. The Arabic Numeral System
3.7. Binary Fixed Point
3.7.1. Limitations of Binary
3.8. Unsigned Binary Integers
3.9. Two's Complement
3.9.1. Format
3.9.2. Negation
3.9.3. Addition and Subtraction
3.9.4. Range
3.9.5. Comparison
3.9.6. Overflow Detection
3.9.7. Extension and Reduction
3.10. Floating Point
3.10.1. The Basics
3.10.2. A Simple Floating Point Format
3.10.3. Overflow and Underflow
3.10.4. Cost of Floating Point
3.11. Character Storage
3.11.1. ASCII
3.11.2. ISO
3.11.3. Unicode
3.12. Homework

    3.1. Motivation

    Knowing the limitations of computer number systems is necessary in order to write programs that produce correct and precise output, and also in writing the most efficient programs possible.