Preview

Informatics in school

Advanced search

Method for extracting square and cube roots in the binary number system

https://doi.org/10.32517/2221-1993-2021-20-1-42-45

Abstract

The article describes in detail the methods of extracting square and cube roots in the binary number system. The method for extracting the square root of a binary number is similar to the corresponding method for decimal numbers, which is called the "column method". As for decimal numbers, when choosing the next digit of the root, twice the current value of the root, represented in the binary system, is used. When extracting the cube root (also "column"), there are two differences from the decimal system. The first is that instead of 300 (the product of 3 and 100), the binary number 1100 is used (that is, the product of the binary equivalents of the numbers 3 and 4). The second difference is that instead of the number 30 (the product of 3 and 10), the binary number 110 is used (that is, the product of binary analogs numbers 3 and 2). To facilitate the selection of the next root digit (0 or 1), a number of standard values have been calculated, depending on the current root value. Assignments for independent work of students are offered.

About the Author

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

Moscow, Russia



References

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

2. Босова Л. Л., Босова А. Ю. Информатика. 10 класс: учебник. М.: БИНОМ. Лаборатория знаний, 2016. 288 с.

3. Двоичная система счисления // Википедия. https://ru.wikipedia.org/wiki/Двоичная_система_счисления

4. Квадратный корень столбиком // Википедия. https://ru.wikipedia.org/wiki/Квадратный_корень#Столбиком

5. Кубический корень столбиком // Википедия. https://ru.wikipedia.org/wiki/Кубический_корень#Столбиком

6. Поляков К. Ю., Еремин Е. А. Информатика. 8 класс: учебник. М.: БИНОМ. Лаборатория знаний, 2019. 256 с.

7. Поляков К. Ю., Еремин Е. А. Информатика. 10 класс. Базовый и углубленный уровни: учебник: в 2 ч. Ч. 1. М.: БИНОМ. Лаборатория знаний, 2016. 352 с.

8. Семакин И. Г., Залогова Г. А., Русаков С. В., Шестакова Л. В. Информатика: учебник для 8 класса. М.: БИНОМ. Лаборатория знаний. 2013. 176 с.


Review

For citations:


Zlatopolski D.M. Method for extracting square and cube roots in the binary number system. Informatics in school. 2021;1(1):42-45. (In Russ.) https://doi.org/10.32517/2221-1993-2021-20-1-42-45

Views: 2068


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2221-1993 (Print)