Numbers and Computers

This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers.

Divided into two parts, the first deals with standard representations of integers and floating point numbers, while the second details several other number representations. Each chapter ends with exercises to review the key points. Topics covered include interval arithmetic, fixed-point numbers, floating point numbers, big integers and rational arithmetic.

This book is for anyone who develops software including software engineerings, scientists, computer science students, engineering students and anyone who programs for fun.

Table of Contents

Part I Standard Representations
Chapter 1 Number Systems
Chapter 2 Integers
Chapter 3 Floating Point

Part II Other Representations
Chapter 4 Big Integers and Rational Arithmetic
Chapter 5 Fixed-Point Numbers
Chapter 6 Decimal Floating Point
Chapter 7 Interval Arithmetic