Number Systems – Fomin

In this post, we will see the book Number Systems by S. V. Fomin. This books is a part of the Popular Lectures in Mathematics series.

About the book

The most common language of numbers, the decimal system, has not always been used universally. From a purely mathematical point of view, the decimal system has no inherent advantages over other possible systems; its popularity is due to historical and biological, not mathematical factors. In this book, S. V. Fomin discusses the origin, properties, and applications of various number systems, including the decimal, the binary, and the ternary. His presentation offers the student an introduction to mathematical abstraction and then, through its examples, shows him the abstraction at work.

The book was translated from Russian by Joan. W. Teller and Thomas P. Branson. The book was published in 1974.

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You can get the book here.

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Preface vii

1. Round and Unrounded Numbers 1
2. The Origin of the Decimal Number System 3
3. Other Number Systems and Their Origins 4
4. Positional and Nonpositional Systems 6
5. Arithmetic Operations in Various Number Systems 7
6. Translating Numbers from One System to Another 9
7. Tests for Divisibility 13
8. The Binary System 17
9. The Game of Nim 20
10. The Binary Code and Telegraphy 25
11. The Binary System—A Guardian of Secrets 26
12. A Few Words about Computers 28
13. Why Electronic Machines “Prefer” the Binary System 29
14. One Remarkable Property of the Ternary System 31
15. On Infinite Number Representations 34

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