# Numbers and Computers

• Ronald T. Kneusel
Textbook

1. Front Matter
Pages i-xiii
2. ### Standard Representations

1. Front Matter
Pages 1-1
2. Ronald T. Kneusel
Pages 3-17
3. Ronald T. Kneusel
Pages 19-79
4. Ronald T. Kneusel
Pages 81-115
5. Ronald T. Kneusel
Pages 117-135
3. ### Other Representations

1. Front Matter
Pages 137-137
2. Ronald T. Kneusel
Pages 139-182
3. Ronald T. Kneusel
Pages 183-213
4. Ronald T. Kneusel
Pages 215-234
5. Ronald T. Kneusel
Pages 235-264
6. Ronald T. Kneusel
Pages 265-292
7. Ronald T. Kneusel
Pages 293-342
4. Back Matter
Pages 343-346

### Introduction

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 examines several other number representations. Details are explained thoroughly, with clarity and specificity. Each chapter ends with a summary, recommendations, carefully selected references, and exercises to review the key points. Topics covered include interval arithmetic, fixed-point numbers, big integers and rational arithmetic. This new edition has three new chapters: Pitfalls of Floating-Point Numbers (and How to Avoid Them), Arbitrary Precision Floating Point, and Other Number Systems.

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

### Keywords

Big integer arithmetic decimal floating point numbers fixed point arithmetic floating point numbers integers interval arithmetic number bases rational arithmetic

#### Authors and affiliations

• Ronald T. Kneusel
• 1
1. 1.BroomfieldUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-50508-4
• Copyright Information Springer International Publishing AG 2017
• Publisher Name Springer, Cham
• eBook Packages Computer Science
• Print ISBN 978-3-319-50507-7
• Online ISBN 978-3-319-50508-4
• Buy this book on publisher's site
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