Перевод числа 00000000000000000000000000000000000000000000001fffffffffffffffff из 0000000000000000000000000000000000000000000000100000000000000000-ой системы счисления в 0000000000000000000000000000000000000000000000100000000000000000-ую

Для перевода числа 00000000000000000000000000000000000000000000001fffffffffffffffff из 0000000000000000000000000000000000000000000000100000000000000000-ой в 0000000000000000000000000000000000000000000000100000000000000000-ую систему счисления, необходимо сначала перевести его в десятичную систему, а полученное число в 0000000000000000000000000000000000000000000000100000000000000000-ую. Для перевода 0000000000000000000000000000000000000000000000100000000000000000-ого числа 00000000000000000000000000000000000000000000001fffffffffffffffff в десятичное необходимо записать его в виде многочлена, состоящего из произведений цифр вида:

A_{0000000000000000000000000000000000000000000000100000000000000000} = a_n-1 ∙ 0000000000000000000000000000000000000000000000100000000000000000^n-1 + a_n-2 ∙ 0000000000000000000000000000000000000000000000100000000000000000^n-2 + ∙∙∙ + a₀ ∙ 0000000000000000000000000000000000000000000000100000000000000000⁰

В результате преобразований получим:

00000000000000000000000000000000000000000000001fffffffffffffffff_{0000000000000000000000000000000000000000000000100000000000000000}=0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁶³ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁶² + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁶¹ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁶⁰ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁵⁹ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁵⁸ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁵⁷ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁵⁶ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁵⁵ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁵⁴ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁵³ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁵² + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁵¹ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁵⁰ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁴⁹ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁴⁸ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁴⁷ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁴⁶ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁴⁵ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁴⁴ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁴³ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁴² + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁴¹ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000⁴⁰ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000³⁹ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000³⁸ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000³⁷ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000³⁶ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000³⁵ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000³⁴ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000³³ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000³² + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000³¹ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000³⁰ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000²⁹ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000²⁸ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000²⁷ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000²⁶ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000²⁵ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000²⁴ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000²³ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000²² + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000²¹ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000²⁰ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000¹⁹ + 0 ∙ 0000000000000000000000000000000000000000000000100000000000000000¹⁸ + 1 ∙ 0000000000000000000000000000000000000000000000100000000000000000¹⁷ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000¹⁶ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000¹⁵ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000¹⁴ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000¹³ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000¹² + f ∙ 0000000000000000000000000000000000000000000000100000000000000000¹¹ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000¹⁰ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000⁹ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000⁸ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000⁷ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000⁶ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000⁵ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000⁴ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000³ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000² + f ∙ 0000000000000000000000000000000000000000000000100000000000000000¹ + f ∙ 0000000000000000000000000000000000000000000000100000000000000000⁰ = 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ 1.0E+306 + 1 ∙ 1.0E+289 + 15 ∙ 1.0E+272 + 15 ∙ 1.0E+255 + 15 ∙ 1.0E+238 + 15 ∙ 1.0E+221 + 15 ∙ 1.0E+204 + 15 ∙ 1.0E+187 + 15 ∙ 1.0E+170 + 15 ∙ 1.0E+153 + 15 ∙ 1.0E+136 + 15 ∙ 1.0E+119 + 15 ∙ 1.0E+102 + 15 ∙ 1.0E+85 + 15 ∙ 1.0E+68 + 15 ∙ 1.0E+51 + 15 ∙ 1.0E+34 + 15 ∙ 100000000000000000 + 15 ∙ 1 = NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + NAN + 0 + 1.0E+289 + 1.5E+273 + 1.5E+256 + 1.5E+239 + 1.5E+222 + 1.5E+205 + 1.5E+188 + 1.5E+171 + 1.5E+154 + 1.5E+137 + 1.5E+120 + 1.5E+103 + 1.5E+86 + 1.5E+69 + 1.5E+52 + 1.5E+35 + 1500000000000000000 + 15 = NAN₁₀

Таким образом:

00000000000000000000000000000000000000000000001fffffffffffffffff_{0000000000000000000000000000000000000000000000100000000000000000} = NAN₁₀.

Для перевода десятичного числа NAN в 0000000000000000000000000000000000000000000000100000000000000000-ую систему счисления, необходимо его последовательно делить на 0000000000000000000000000000000000000000000000100000000000000000 до тех пор, пока остаток не станет меньше чем 0000000000000000000000000000000000000000000000100000000000000000.

Ответом будет являться обратная последовательность результатов деления:

0₁₀=0_{0000000000000000000000000000000000000000000000100000000000000000}

Окончательный ответ будет выглядеть так:

00000000000000000000000000000000000000000000001fffffffffffffffff_{0000000000000000000000000000000000000000000000100000000000000000}=0_{0000000000000000000000000000000000000000000000100000000000000000}