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Numbers and Computers

  • Textbook
  • © 2017

Overview

Authors:
  1. Ronald T. Kneusel

    1. Broomfield, USA

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  • Explores how computers use numbers to complete operations
  • Includes exercises and examples that are code snippets in C or Python
  • Covers IEEE 754 on Floating Point Arithmetic
  • Includes supplementary material: sn.pub/extras

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Standard Representations

    1. Front Matter

      Pages 1-1
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    2. Number Systems

      • Ronald T. Kneusel
      Pages 3-17

    3. Integers

      • Ronald T. Kneusel
      Pages 19-79

    4. Floating Point

      • Ronald T. Kneusel
      Pages 81-115

    5. Pitfalls of Floating-Point Numbers (and How to Avoid Them)

      • Ronald T. Kneusel
      Pages 117-135

  3. Other Representations

    1. Front Matter

      Pages 137-137
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    2. Big Integers and Rational Arithmetic

      • Ronald T. Kneusel
      Pages 139-182

    3. Fixed-Point Numbers

      • Ronald T. Kneusel
      Pages 183-213

    4. Decimal Floating Point

      • Ronald T. Kneusel
      Pages 215-234

    5. Interval Arithmetic

      • Ronald T. Kneusel
      Pages 235-264

    6. Arbitrary Precision Floating-Point

      • Ronald T. Kneusel
      Pages 265-292

    7. Other Number Systems

      • Ronald T. Kneusel
      Pages 293-342

  4. Back Matter

    Pages 343-346
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Keywords

About this book

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.

Reviews

“Kneusel offers a book for all these audiences, and for anyone who would like to delve deeper into this branch of technology. … This book should be an excellent resource in the classroom. It can serve as a good reference for future use and can also be used very profitably for self-study.” (Edgar R. Chavez, Computing Reviews, May, 2018)​

Authors and Affiliations

  • Broomfield, USA

    Ronald T. Kneusel

About the author

Dr. Ronald T. Kneusel is a Senior Data Scientist with Harris Corportation. He received his Ph.D. in Computer Science from the University of Colorado, Boulder, in machine learning, and his M.S. in Physics from Michigan State University. His background includes work in breast cancer research and early functional MRI (Medical College of Wisconsin) through medical device development (MR, CT, US) to medical imaging and remote sensing image analysis. He has been deeply involved with software development at all levels since his first forays with an 8-bit Apple II+ computer in the early 1980s hooked him for life. Dr. Kneusel is currently working with Harris Corporation on the application of modern machine learning techniques to remote sensing imagery and related modalities. He is the author of multiple peer-reviewed research articles.

Bibliographic Information

  • Book Title: Numbers and Computers

  • Authors: Ronald T. Kneusel

  • DOI: https://doi.org/10.1007/978-3-319-50508-4

  • Publisher: Springer Cham

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-50507-7Published: 17 February 2017

  • Softcover ISBN: 978-3-319-84415-2Published: 13 July 2018

  • eBook ISBN: 978-3-319-50508-4Published: 09 February 2017

  • Edition Number: 2

  • Number of Pages: XIII, 346

  • Number of Illustrations: 56 b/w illustrations, 12 illustrations in colour

  • Topics: Arithmetic and Logic Structures, Numeric Computing

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