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Non-standard methods for converting numbers from one number system to another

https://doi.org/10.32517/2221-1993-2020-19-9-28-30

Abstract

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.

About the Author

D. M. Zlatopolski
School 1530 “Lomonosov School”
Russian Federation


References

1. Андреева Е. В., Босова Л. Л., Фалина И. Н. Математические основы информатики. М.: БИНОМ. Лаборатория

2. знаний, 2005. 328 с.

3. Гашков С. Б. Занимательная компьютерная арифметика.

4. Математика и искусство счета на компьютерах и без них. М.:

5. URSS, 2017. 448 с.

6. Златопольский Д.М., Шилов В.В. Из истории двоичной

7. системы счисления. Томас Харриот // Информатика в школе.

8. № 6. C. 19–23. DOI: 10.32517/2221-1993-2020-19-6-19-23

9. Схема Горнера. https://ru.wikipedia.org/wiki/Схема_Горнера

10. Legendre A. M. Essai sur la theorie des nombres. Paris,

11. Р. 229.


Review

For citations:


Zlatopolski D.M. Non-standard methods for converting numbers from one number system to another. Informatics in school. 2020;1(9):28-30. (In Russ.) https://doi.org/10.32517/2221-1993-2020-19-9-28-30

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ISSN 2221-1993 (Print)