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Задать вопрос экспертам

Консультация № 188652

16.01.2016, 22:47

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0 1 1

Образование

Здравствуйте! Прошу помощи в следующем вопросе:
Иван обнаружил на доске две колонки чисел, и догадался, что в левой колонке записаны числа в десятичной системе счисления, а в правой – в некоторой нетривиальной системе счисления. Помогите Ивану преобразовать число 36 в эту нетривиальную систему счисления.
1 1
2 10
3 100
4 101
5 1000
13 100000
17 100101
27 1001001

Обсуждение

давно

Гордиенко Андрей Владимирович

Мастер-Эксперт
17387
18345

17.01.2016, 08:59

общий

это ответ

Здравствуйте, Посетитель - 399097!

Учитывая представление чисел 1, 2, 3, 5, 13 в заданной нетривиальной системе счисления, можно предположить, что эти числа образуют базис данной системы. По-видимому,
8 10000
21 1000000
34 10000000
Скорее всего, имеется в виду фибоначчиева система счисления. Тогда число 36 можно представить несколькими способами. Например,
36=21+13+2=1*21+1*13+0*8+0*5+0*3+1*2+0*1=1100010_f,
36=21+8+5+2=1*21+0*13+1*8+1*5+0*3+1*2+0*1=1011010_f,
36=34+2=1*34+0*21+0*13+0*8+0*5+0*3+1*2+0*1=10000010_f.

С уважением.

Об авторе:
Facta loquuntur.

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