The Number Systems
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The Number Systems Foundations Of Algebra And Analysis
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Author : Solomon Feferman
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
The Number Systems Foundations Of Algebra And Analysis written by Solomon Feferman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
The subject of this book is the successive construction and development of the basic number systems of mathematics: positive integers, integers, rational numbers, real numbers, and complex numbers. This second edition expands upon the list of suggestions for further reading in Appendix III. From the Preface: ``The present book basically takes for granted the non-constructive set-theoretical foundation of mathematics, which is tacitly if not explicitly accepted by most working mathematicians but which I have since come to reject. Still, whatever one's foundational views, students must be trained in this approach in order to understand modern mathematics. Moreover, most of the material of the present book can be modified so as to be acceptable under alternative constructive and semi-constructive viewpoints, as has been demonstrated in more advanced texts and research articles.''
The Number Systems And Operations Of Arithmetic
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Author : Orval M. Klose
language : en
Publisher: Elsevier
Release Date : 2014-05-16
The Number Systems And Operations Of Arithmetic written by Orval M. Klose and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-16 with Mathematics categories.
The Number Systems and Operations of Arithmetic was written for the single purpose of explaining to elementary school teachers (both in-service and in-training) the nature of those basic principles of mathematics which form the foundations and structural framework of arithmetic, and how the familiar formal algorithms of arithmetic stem from these structural principles. The book is organized into two parts. Part I on number systems covers the origin of numerical thinking; natural operations with the natural numbers; natural laws for the natural operations; the inverse operations and convergence and the number systems generated by these operations; and classification of the number systems as abstract systems. Part II on computational algorithms discusses computations with natural numbers, rational numbers, real numbers, and complex numbers. The ""answers"" to all the exercises are also provided in the main body of the text and it is hoped that the student will form the habit of looking there for them.
The Number Systems Of Analysis
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Author : Charles Little
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-09-05
The Number Systems Of Analysis written by Charles Little and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-05 with Mathematics categories.
Although students of analysis are familiar with real and complex numbers, few treatments of analysis deal with the development of such numbers in any depth. An understanding of number systems at a fundamental level is necessary for a deeper grasp of analysis. Beginning with elementary concepts from logic and set theory, this book develops in turn the natural numbers, the integers and the rational, real and complex numbers. The development is motivated by the need to solve polynomial equations, and the book concludes by proving that such equations have solutions in the complex number system.
Cultural Number Systems
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Author : Karenleigh A. Overmann
language : en
Publisher: Springer Nature
Release Date : 2025-04-26
Cultural Number Systems written by Karenleigh A. Overmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-26 with Social Science categories.
This sourcebook presents an extensive look at cultural number systems in numeracy and writing systems. Based on a decade of research by the author, the work examines topics such as why Xerxes the First counted his army by having his men march through an enclosure big enough to hold 10,000 of them at a time, why the Hawaiian word for "twenty" means “nine and two,” why an ancient Greek mathematician was driven mad by irrational numbers, and how old counting might be and how we might know this. Along the way, the author describes topics such as dactylonomy, the ancient art of expressing and calculating numbers with the fingers; specified counting, the use of different counting sequences to count different types of objects; and the ephemeral abacus, strategies for counting that involve people and goods but not an actual device. The chapters are organized into six geographical areas (the ancient Near East, Africa, Europe, Asia/India, Oceania, and the Americas).
Residue Number Systems
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Author : Amos R. Omondi
language : en
Publisher: Imperial College Press
Release Date : 2007
Residue Number Systems written by Amos R. Omondi and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Technology & Engineering categories.
Residue number systems (RNSs) and arithmetic are useful for several reasons. First, a great deal of computing now takes place in embedded processors, such as those found in mobile devices, for which high speed and low-power consumption are critical; the absence of carry propagation facilitates the realization of high-speed, low-power arithmetic. Second, computer chips are now getting to be so dense that full testing will no longer be possible; so fault tolerance and the general area of computational integrity have become more important. RNSs are extremely good for applications such as digital signal processing, communications engineering, computer security (cryptography), image processing, speech processing, and transforms, all of which are extremely important in computing today. This book provides an up-to-date account of RNSs and arithmetic. It covers the underlying mathematical concepts of RNSs; the conversion between conventional number systems and RNSs; the implementation of arithmetic operations; various related applications are also introduced. In addition, numerous detailed examples and analysis of different implementations are provided. Sample Chapter(s). Chapter 1: Introduction (301 KB). Contents: Introduction; Mathematical Fundamentals; Forward Conversion; Addition; Multiplication; Comparison, Overflow-Detection, Sign-Determination, Scaling, and Division; Reverse Conversion; Applications. Readership: Graduate students, academics and researchers in computer engineering and electrical & electronic engineering.
Number Systems
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Author : Anthony Kay
language : en
Publisher: CRC Press
Release Date : 2025-09-04
Number Systems written by Anthony Kay and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-09-04 with Mathematics categories.
Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs. The book continually seeks to build upon students' intuitive ideas of how numbers and arithmetic work, and to guide them towards the means to embed this natural understanding into a more structured framework of understanding. The author’s motivation for writing this book is that most previous texts, which have complete coverage of the subject, have not provided the level of explanation needed for first-year students. On the other hand, those that do give good explanations tend to focus broadly on Foundations or Analysis and provide incomplete coverage of Number Systems. Features Approachable for first year undergraduates, but still of interest to more advanced students and postgraduates Does not merely present definitions, theorems and proofs, but also motivates them in terms of intuitive knowledge and discusses methods of proof Draws attention to connections with other areas of mathematics Plenty of exercises for students, both straightforward problems and more in-depth investigations Introduces many concepts that are required in more advanced topics in mathematics New to the second edition Complete solutions to all exercises, and hints for the in-depth investigations Extensive changes to chapters 4 and 5, including defining integral domains as distinct from commutative rings, a more complete discussion of irreducibles, primes and unique factorisation, and more topics in elementary number theory A completely revised chapter 8, giving a more coherent account of quadratic rings and their unique (or non-unique) factorisation properties A thorough correction of typos and errors across all chapters Updates to the bibliography
Number Systems For Deep Neural Network Architectures
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Author : Ghada Alsuhli
language : en
Publisher: Springer Nature
Release Date : 2023-09-01
Number Systems For Deep Neural Network Architectures written by Ghada Alsuhli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-01 with Technology & Engineering categories.
This book provides readers a comprehensive introduction to alternative number systems for more efficient representations of Deep Neural Network (DNN) data. Various number systems (conventional/unconventional) exploited for DNNs are discussed, including Floating Point (FP), Fixed Point (FXP), Logarithmic Number System (LNS), Residue Number System (RNS), Block Floating Point Number System (BFP), Dynamic Fixed-Point Number System (DFXP) and Posit Number System (PNS). The authors explore the impact of these number systems on the performance and hardware design of DNNs, highlighting the challenges associated with each number system and various solutions that are proposed for addressing them.
The Person Number Systems Of Sweden Norway Denmark And Israel
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Author : Anders Steen Lunde
language : en
Publisher:
Release Date : 1980
The Person Number Systems Of Sweden Norway Denmark And Israel written by Anders Steen Lunde and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Reference categories.
Finite Precision Number Systems And Arithmetic
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Author : Peter Kornerup
language : en
Publisher: Cambridge University Press
Release Date : 2010-09-30
Finite Precision Number Systems And Arithmetic written by Peter Kornerup and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-30 with Mathematics categories.
This comprehensive reference volume, suitable for graduate teaching, includes problems, exercises, solutions and an extensive bibliography.
Introduction To It Systems With Number System Covered Aicte Model Curriculum And Syllabus
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Author : Dr. Chetna Devkar
language : en
Publisher: Academic Guru Publishing House
Release Date : 2025-02-10
Introduction To It Systems With Number System Covered Aicte Model Curriculum And Syllabus written by Dr. Chetna Devkar and has been published by Academic Guru Publishing House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-10 with Study Aids categories.
Introduction to IT Systems with Number Systems is an essential resource for students studying Information Technology, especially those following the AICTE Model Curriculum and Syllabus. The book presents a comprehensive overview of the key concepts, tools, and techniques that form the backbone of modem IT systems. It covers a wide range of topics, starting with an introduction to computer systems, operating systems, and information security best practices, before diving into more complex subjects like Boolean algebra and digital logic. The book begins by revisiting the number system and base conversions, laying the groundwork for understanding binary codes and their significance in computing. It then introduces Boolean functions and logic gates, essential for understanding digital circuits. Key topics such as simplifying Boolean functions, Karnaugh maps, and NAND-NOR implementations are explored in detail, ensuring students develop a strong grasp of logical reasoning required in the design and operation of digital systems. In addition to theoretical content, the book emphasizes practical applications. It provides clear examples, exercises, and case studies that help students relate abstract concepts to real-world scenarios. The section on information security best practices equips students with essential skills for protecting information in today’s digital world. Overall, this book is a valuable resource that equips students with the knowledge and skills necessary to excel in the rapidly evolving field of Information Technology.