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E-raamat: Numbers and Computers

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 14-Apr-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319172606
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Numbers and ComputersSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 14-Apr-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319172606
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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.

Arvustused

"This book can be profitably read by anyone who is interested in computers and is willing to occasionally slog through perhaps unfamiliar territory with minimal guidance. ... details are explained thoroughly, with utmost clarity and specificity. Each chapter ends with a summary, recommendations, exercises, and a set of carefully selected references. This small book provides a solid foundation for further exploration and study. It can be especially valuable to computer science and electrical engineering students." (Edgar R. Chavez, Computing Reviews, February, 2016) "This book is, on one level, a discussion of how computers work with numbers. It tells how computers represent numbers such as integers, floating point numbers, big integers, decimals, and what is more, how one can write one's own routines to operate on numbers. ... If this makes you wonder about the utility of computers and how to better understand numerical representations and calculations, you will do well to add this book to your winter reading list." (David S. Mazel, MAA Reviews, maa.org, January, 2016) "The book starts with an overview on number systems. ... The book is a good source of information for all who wants to learn how numbers are represented in computers and how computations are performed." (Michael Jung, zbMATH 1330.65002, 2016) "This book ... should be on the bookshelf of every software developer. ... Each chapter has a nicely composed set of exercises and a well-constructed set of references. The book contains numerous algorithmic examples presented throughout the text in C-like code that is easy to follow, as well as a well-organized index. ... Summing Up: Recommended. Upper-division undergraduates, graduate students, researchers/faculty, two-year technical program students, and professionals/practitioners." (J. Beidler, Choice, Vol.53 (4), December, 2015)

Part I Standard Representations
1 Number Systems
3(16)
1.1 Representing Numbers
3(5)
1.2 The Big Three (and One Old Guy)
8(2)
1.3 Converting Between Number Bases
10(6)
1.4
Chapter Summary
16(1)
Exercises
16(1)
References
16(3)
2 Integers
19(56)
2.1 Bits, Nibbles, Bytes, and Words
19(2)
2.2 Unsigned Integers
21(4)
2.2.1 Representation
22(1)
2.2.2 Storage in Memory: Endianness
22(3)
2.3 Operations on Unsigned Integers
25(28)
2.3.1 Bitwise Logical Operations
25(5)
2.3.2 Testing, Setting, Clearing, and Toggling Bits
30(3)
2.3.3 Shifts and Rotates
33(4)
2.3.4 Comparisons
37(4)
2.3.5 Arithmetic
41(11)
2.3.6 Square Roots
52(1)
2.4 What About Negative Integers'?
53(3)
2.4.1 Sign-Magnitude
54(1)
2.4.2 One's Complement
54(1)
2.4.3 Two's Complement
55(1)
2.5 Operations on Signed Integers
56(10)
2.5.1 Comparison
56(1)
2.5.2 Arithmetic
57(9)
2.6 Binary-Coded Decimal
66(6)
2.6.1 Introduction
66(2)
2.6.2 Arithmetic with BCD
68(1)
2.6.3 Conversion Routines
69(3)
2.7
Chapter Summary
72(1)
Exercises
73(1)
References
74(1)
3 Floating point
75(40)
3.1 Floating-Point Numbers
75(3)
3.2 An Exceedingly Brief History of Floating-Point Numbers
78(2)
3.3 Comparing Floating-Point Representations
80(3)
3.4 IEEE 754 Floating-Point Representations
83(6)
3.5 Rounding Floating-Point Numbers (IEEE 754)
89(4)
3.6 Comparing Floating-Point Numbers (IEEE 754)
93(2)
3.7 Basic Arithmetic (IEEE 754)
95(3)
3.8 Handling Exceptions (IEEE 754)
98(3)
3.9 Floating-Point Hardware (IEEE 754)
101(2)
3.10 The Elephant in the Living Room (Pitfalls of Floating Point)
103(6)
3.11
Chapter Summary
109(1)
Exercises
109(2)
References
111(4)
Part II Other Representations
4 Big Integers and Rational Arithmetic
115(42)
4.1 What is a Big Integer?
115(1)
4.2 Representing Big Integers
116(6)
4.3 Arithmetic with Big Integers
122(12)
4.4 Alternative Multiplication and Division Routines
134(9)
4.5 Implementations
143(3)
4.6 Rational Arithmetic with Big Integers
146(6)
4.7 When to Use Big Integers and Rational Arithmetic
152(2)
4.8
Chapter Summary
154(1)
Exercises
155(1)
References
156(1)
5 Fixed-Point Numbers
157(24)
5.1 Representation (Q Notation)
157(5)
5.2 Arithmetic with Fixed-Point Numbers
162(5)
5.3 Trigonometric and Other Functions
167(10)
5.4 When to Use Fixed-Point Numbers
177(1)
5.5
Chapter Summary
177(1)
Exercises
178(1)
References
179(2)
6 Decimal Floating Point
181(20)
6.1 What Is Decimal Floating-Point?
181(1)
6.2 The IEEE 754-2008 Decimal Floating-Point Format
182(7)
6.3 Decimal Floating-Point in Software
189(9)
6.4 Thoughts on Decimal Floating-Point
198(1)
6.5
Chapter Summary
199(1)
Exercises
199(1)
References
199(2)
7 Interval Arithmetic
201(28)
7.1 Denning Intervals
201(2)
7.2 Basic Operations
203(14)
7.3 Functions and Intervals
217(5)
7.4 Implementations
222(4)
7.5 Thoughts on Interval Arithmetic
226(1)
7.6
Chapter Summary
227(1)
Exercises
227(1)
References
227(2)
Index 229
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