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Numbers and Computers Second Edition 2017 [Kõva köide]

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  • Formaat: Hardback, 346 pages, kõrgus x laius: 235x155 mm, kaal: 6623 g, 12 Illustrations, color; 56 Illustrations, black and white; XIII, 346 p. 68 illus., 12 illus. in color., 1 Hardback
  • Ilmumisaeg: 17-Feb-2017
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319505076
  • ISBN-13: 9783319505077
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Numbers and Computers Second Edition 2017Suurem pilt
  • Formaat: Hardback, 346 pages, kõrgus x laius: 235x155 mm, kaal: 6623 g, 12 Illustrations, color; 56 Illustrations, black and white; XIII, 346 p. 68 illus., 12 illus. in color., 1 Hardback
  • Ilmumisaeg: 17-Feb-2017
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319505076
  • ISBN-13: 9783319505077
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319505077.html
Märksõnad:
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 chapter

s: 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.

Number Systems.- Integers.- Floating Point.- Pitfalls of Floating-Point Numbers (and How to Avoid Them).- Big Integers and Rational Arithmetic.- Fixed-Point Numbers.- Decimal Floating Point.- Interval Arithmetic.- Arbitrary Precision Floating-Point.- Other Number Systems.

Arvustused

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)

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(3)
Exercises
16(1)
References
17(2)
2 Integers
19(62)
2.1 Bits, Nibbles, Bytes, and Words
19(2)
2.2 Unsigned Integers
21(4)
2.2.1 Representation
21(1)
2.2.2 Storage in Memory: Endianness
22(3)
2.3 Operations on Unsigned Integers
25(29)
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(2)
2.4 What About Negative Integers?
54(2)
2.4.1 Sign-Magnitude
54(1)
2.4.2 One's Complement
55(1)
2.4.3 Two's Complement
55(1)
2.5 Operations on Signed Integers
56(11)
2.5.1 Comparison
56(2)
2.5.2 Arithmetic
58(9)
2.6 Binary-Coded Decimal
67(9)
2.6.1 Introduction
67(2)
2.6.2 Arithmetic with BCD
69(1)
2.6.3 Conversion Routines
70(3)
2.6.4 Other BCD Encodings
73(3)
2.7
Chapter Summary
76(5)
Exercises
77(2)
References
79(2)
3 Floating Point
81(36)
3.1 Floating-Point Numbers
81(3)
3.2 An Exceedingly Brief History of Floating-Point Numbers
84(1)
3.3 Comparing Floating-Point Representations
85(4)
3.4 IEEE 754 Floating-Point Representations
89(8)
3.5 Rounding Floating-Point Numbers (IEEE 754)
97(3)
3.6 Comparing Floating-Point Numbers (IEEE 754)
100(2)
3.7 Basic Arithmetic (IEEE 754)
102(3)
3.8 Handling Exceptions (IEEE 754)
105(3)
3.9 Floating-Point Hardware (IEEE 754)
108(2)
3.10 Binary Coded Decimal Floating-Point Numbers
110(3)
3.11
Chapter Summary
113(4)
Exercises
114(1)
References
115(2)
4 Pitfalls of Floating-Point Numbers (and How to Avoid Them)
117(22)
4.1 What Pitfalls?
117(2)
4.2 Some Experiments
119(11)
4.3 Avoiding the Pitfalls
130(4)
4.4
Chapter Summary
134(5)
Exercises
135(1)
References
135(4)
Part II Other Representations
5 Big Integers and Rational Arithmetic
139(44)
5.1 What is a Big Integer?
139(1)
5.2 Representing Big Integers
140(6)
5.3 Arithmetic with Big Integers
146(12)
5.4 Alternative Multiplication and Division Routines
158(9)
5.5 Implementations
167(4)
5.6 Rational Arithmetic with Big Integers
171(6)
5.7 When to Use Big Integers and Rational Arithmetic
177(3)
5.8
Chapter Summary
180(3)
Exercises
180(1)
References
181(2)
6 Fixed-Point Numbers
183(32)
6.1 Representation (Q Notation)
183(5)
6.2 Arithmetic with Fixed-Point Numbers
188(6)
6.3 Trigonometric and Other Functions
194(10)
6.4 An Emerging Use Case
204(7)
6.5 When to Use Fixed-Point Numbers
211(1)
6.6
Chapter Summary
212(3)
Exercises
212(1)
References
213(2)
7 Decimal Floating Point
215(20)
7.1 What is Decimal Floating-Point?
215(1)
7.2 The IEEE 754-2008 Decimal Floating-Point Format
216(9)
7.3 Decimal Floating-Point in Software
225(7)
7.4 Thoughts on Decimal Floating-Point
232(1)
7.5
Chapter Summary
233(2)
Exercises
234(1)
References
234(1)
8 Interval Arithmetic
235(30)
8.1 Defining Intervals
235(2)
8.2 Basic Operations
237(16)
8.3 Functions and Intervals
253(5)
8.4 Implementations
258(4)
8.5 Thoughts on Interval Arithmetic
262(1)
8.6
Chapter Summary
263(2)
Exercises
263(1)
References
263(2)
9 Arbitrary Precision Floating-Point
265(28)
9.1 What is Arbitrary Precision Floating-Point?
265(1)
9.2 Representing Arbitrary Precision Floating-Point Numbers
265(5)
9.3 Basic Arithmetic with Arbitrary Precision Floating-Point Numbers
270(3)
9.4 Comparison and Other Methods
273(1)
9.5 Trigonometric and Transcendental Functions
274(4)
9.6 Arbitrary Precision Floating-Point Libraries
278(12)
9.7 Thoughts on Arbitrary Precision Floating-Point
290(1)
9.8
Chapter Summary
291(2)
Exercises
291(1)
References
292(1)
10 Other Number Systems
293(50)
10.1 Introduction
293(1)
10.2 Logarithmic Number System
293(14)
10.3 Double-Base Number System
307(17)
10.4 Residue Number System
324(8)
10.5 Redundant Signed-Digit Number System
332(7)
10.6
Chapter Summary
339(4)
Exercises
340(1)
References
341(2)
Index 343
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.