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Conversion to binary number system of some types of ordinary fractions

https://doi.org/10.32517/2221-1993-2020-19-10-42-44

Abstract

The article describes a technique developed by the author for converting a number of ordinary fractions into a binary number system without intermediate conversion to decimal. The technique is generally applicable to two types of fractions: the denominator of which is 2n – 1 or 2n + 1, where n is a natural number, and also for denominator values 2, 4, 8, ... times greater than the indicated values. For fractions with a denominator of the form 2n + 1 and numerators equal to powers of two, an original technique is implemented during translation, which consists in using a conditional negative digit 1 (its designation: 1). The analysis showed that the developed method is more effective than the traditional one. A large number of examples are given and assignments for independent work of students are proposed.

About the Author

D. M. Zlatopolski
School 1530 "Lomonosov School"
Russian Federation
Moscow


References

1. Андреева Е. В., Босова Л. Л., Фалина И. Н. Математические основы информатики. М.: БИНОМ. Лаборатория знаний, 2005. 328 с.

2. Note sur l’arithmetique binaire // Journal de mathematiques elementaires. 1897. Р. 148–151.


Review

For citations:


Zlatopolski D.M. Conversion to binary number system of some types of ordinary fractions. Informatics in school. 2020;(10):42-44. (In Russ.) https://doi.org/10.32517/2221-1993-2020-19-10-42-44

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ISSN 2221-1993 (Print)