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.
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