Перевод числа 100100011010101010010010101001001010101010100110010101010000010101110010010001010100100101010100101010101000101010000100101001 из 10010101010010-ой системы счисления в 10010010101001010101010100100100-ую

Для перевода числа 100100011010101010010010101001001010101010100110010101010000010101110010010001010100100101010100101010101000101010000100101001 из 10010101010010-ой в 10010010101001010101010100100100-ую систему счисления, необходимо сначала перевести его в десятичную систему, а полученное число в 10010010101001010101010100100100-ую. Для перевода 10010101010010-ого числа 100100011010101010010010101001001010101010100110010101010000010101110010010001010100100101010100101010101000101010000100101001 в десятичное необходимо записать его в виде многочлена, состоящего из произведений цифр вида:

A_{10010101010010} = a_n-1 ∙ 10010101010010^n-1 + a_n-2 ∙ 10010101010010^n-2 + ∙∙∙ + a₀ ∙ 10010101010010⁰

В результате преобразований получим:

100100011010101010010010101001001010101010100110010101010000010101110010010001010100100101010100101010101000101010000100101001_{10010101010010}=1 ∙ 10010101010010¹²⁵ + 0 ∙ 10010101010010¹²⁴ + 0 ∙ 10010101010010¹²³ + 1 ∙ 10010101010010¹²² + 0 ∙ 10010101010010¹²¹ + 0 ∙ 10010101010010¹²⁰ + 0 ∙ 10010101010010¹¹⁹ + 1 ∙ 10010101010010¹¹⁸ + 1 ∙ 10010101010010¹¹⁷ + 0 ∙ 10010101010010¹¹⁶ + 1 ∙ 10010101010010¹¹⁵ + 0 ∙ 10010101010010¹¹⁴ + 1 ∙ 10010101010010¹¹³ + 0 ∙ 10010101010010¹¹² + 1 ∙ 10010101010010¹¹¹ + 0 ∙ 10010101010010¹¹⁰ + 1 ∙ 10010101010010¹⁰⁹ + 0 ∙ 10010101010010¹⁰⁸ + 0 ∙ 10010101010010¹⁰⁷ + 1 ∙ 10010101010010¹⁰⁶ + 0 ∙ 10010101010010¹⁰⁵ + 0 ∙ 10010101010010¹⁰⁴ + 1 ∙ 10010101010010¹⁰³ + 0 ∙ 10010101010010¹⁰² + 1 ∙ 10010101010010¹⁰¹ + 0 ∙ 10010101010010¹⁰⁰ + 1 ∙ 10010101010010⁹⁹ + 0 ∙ 10010101010010⁹⁸ + 0 ∙ 10010101010010⁹⁷ + 1 ∙ 10010101010010⁹⁶ + 0 ∙ 10010101010010⁹⁵ + 0 ∙ 10010101010010⁹⁴ + 1 ∙ 10010101010010⁹³ + 0 ∙ 10010101010010⁹² + 1 ∙ 10010101010010⁹¹ + 0 ∙ 10010101010010⁹⁰ + 1 ∙ 10010101010010⁸⁹ + 0 ∙ 10010101010010⁸⁸ + 1 ∙ 10010101010010⁸⁷ + 0 ∙ 10010101010010⁸⁶ + 1 ∙ 10010101010010⁸⁵ + 0 ∙ 10010101010010⁸⁴ + 1 ∙ 10010101010010⁸³ + 0 ∙ 10010101010010⁸² + 0 ∙ 10010101010010⁸¹ + 1 ∙ 10010101010010⁸⁰ + 1 ∙ 10010101010010⁷⁹ + 0 ∙ 10010101010010⁷⁸ + 0 ∙ 10010101010010⁷⁷ + 1 ∙ 10010101010010⁷⁶ + 0 ∙ 10010101010010⁷⁵ + 1 ∙ 10010101010010⁷⁴ + 0 ∙ 10010101010010⁷³ + 1 ∙ 10010101010010⁷² + 0 ∙ 10010101010010⁷¹ + 1 ∙ 10010101010010⁷⁰ + 0 ∙ 10010101010010⁶⁹ + 0 ∙ 10010101010010⁶⁸ + 0 ∙ 10010101010010⁶⁷ + 0 ∙ 10010101010010⁶⁶ + 0 ∙ 10010101010010⁶⁵ + 1 ∙ 10010101010010⁶⁴ + 0 ∙ 10010101010010⁶³ + 1 ∙ 10010101010010⁶² + 0 ∙ 10010101010010⁶¹ + 1 ∙ 10010101010010⁶⁰ + 1 ∙ 10010101010010⁵⁹ + 1 ∙ 10010101010010⁵⁸ + 0 ∙ 10010101010010⁵⁷ + 0 ∙ 10010101010010⁵⁶ + 1 ∙ 10010101010010⁵⁵ + 0 ∙ 10010101010010⁵⁴ + 0 ∙ 10010101010010⁵³ + 1 ∙ 10010101010010⁵² + 0 ∙ 10010101010010⁵¹ + 0 ∙ 10010101010010⁵⁰ + 0 ∙ 10010101010010⁴⁹ + 1 ∙ 10010101010010⁴⁸ + 0 ∙ 10010101010010⁴⁷ + 1 ∙ 10010101010010⁴⁶ + 0 ∙ 10010101010010⁴⁵ + 1 ∙ 10010101010010⁴⁴ + 0 ∙ 10010101010010⁴³ + 0 ∙ 10010101010010⁴² + 1 ∙ 10010101010010⁴¹ + 0 ∙ 10010101010010⁴⁰ + 0 ∙ 10010101010010³⁹ + 1 ∙ 10010101010010³⁸ + 0 ∙ 10010101010010³⁷ + 1 ∙ 10010101010010³⁶ + 0 ∙ 10010101010010³⁵ + 1 ∙ 10010101010010³⁴ + 0 ∙ 10010101010010³³ + 1 ∙ 10010101010010³² + 0 ∙ 10010101010010³¹ + 0 ∙ 10010101010010³⁰ + 1 ∙ 10010101010010²⁹ + 0 ∙ 10010101010010²⁸ + 1 ∙ 10010101010010²⁷ + 0 ∙ 10010101010010²⁶ + 1 ∙ 10010101010010²⁵ + 0 ∙ 10010101010010²⁴ + 1 ∙ 10010101010010²³ + 0 ∙ 10010101010010²² + 1 ∙ 10010101010010²¹ + 0 ∙ 10010101010010²⁰ + 0 ∙ 10010101010010¹⁹ + 0 ∙ 10010101010010¹⁸ + 1 ∙ 10010101010010¹⁷ + 0 ∙ 10010101010010¹⁶ + 1 ∙ 10010101010010¹⁵ + 0 ∙ 10010101010010¹⁴ + 1 ∙ 10010101010010¹³ + 0 ∙ 10010101010010¹² + 0 ∙ 10010101010010¹¹ + 0 ∙ 10010101010010¹⁰ + 0 ∙ 10010101010010⁹ + 1 ∙ 10010101010010⁸ + 0 ∙ 10010101010010⁷ + 0 ∙ 10010101010010⁶ + 1 ∙ 10010101010010⁵ + 0 ∙ 10010101010010⁴ + 1 ∙ 10010101010010³ + 0 ∙ 10010101010010² + 0 ∙ 10010101010010¹ + 1 ∙ 10010101010010⁰ = 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ 1.0234922944074E+299 + 0 ∙ 1.0224595070359E+286 + 1 ∙ 1.0214277618312E+273 + 0 ∙ 1.0203970577418E+260 + 0 ∙ 1.019367393717E+247 + 0 ∙ 1.0183387687073E+234 + 1 ∙ 1.0173111816644E+221 + 0 ∙ 1.0162846315408E+208 + 1 ∙ 1.0152591172901E+195 + 0 ∙ 1.0142346378672E+182 + 1 ∙ 1.0132111922277E+169 + 0 ∙ 1.0121887793285E+156 + 0 ∙ 1.0111673981275E+143 + 0 ∙ 1.0101470475835E+130 + 0 ∙ 1.0091277266567E+117 + 1 ∙ 1.008109434308E+104 + 0 ∙ 1.0070921694995E+91 + 0 ∙ 1.0060759311943E+78 + 1 ∙ 1.0050607183566E+65 + 0 ∙ 1.0040465299517E+52 + 1 ∙ 1.0030333649457E+39 + 0 ∙ 1.002021222306E+26 + 0 ∙ 10010101010010 + 1 ∙ 1 = INF + NAN + NAN + INF + NAN + NAN + NAN + INF + INF + NAN + INF + NAN + INF + NAN + INF + NAN + INF + NAN + NAN + INF + NAN + NAN + INF + NAN + INF + NAN + INF + NAN + NAN + INF + NAN + NAN + INF + NAN + INF + NAN + INF + NAN + INF + NAN + INF + NAN + INF + NAN + NAN + INF + INF + NAN + NAN + INF + NAN + INF + NAN + INF + NAN + INF + NAN + NAN + NAN + NAN + NAN + INF + NAN + INF + NAN + INF + INF + INF + NAN + NAN + INF + NAN + NAN + INF + NAN + NAN + NAN + INF + NAN + INF + NAN + INF + NAN + NAN + INF + NAN + NAN + INF + NAN + INF + NAN + INF + NAN + INF + NAN + NAN + INF + NAN + INF + NAN + INF + NAN + 1.0234922944074E+299 + 0 + 1.0214277618312E+273 + 0 + 0 + 0 + 1.0173111816644E+221 + 0 + 1.0152591172901E+195 + 0 + 1.0132111922277E+169 + 0 + 0 + 0 + 0 + 1.008109434308E+104 + 0 + 0 + 1.0050607183566E+65 + 0 + 1.0030333649457E+39 + 0 + 0 + 1 = NAN₁₀

Таким образом:

100100011010101010010010101001001010101010100110010101010000010101110010010001010100100101010100101010101000101010000100101001_{10010101010010} = NAN₁₀.

Для перевода десятичного числа NAN в 10010010101001010101010100100100-ую систему счисления, необходимо его последовательно делить на 10010010101001010101010100100100 до тех пор, пока остаток не станет меньше чем 10010010101001010101010100100100.

Ответом будет являться обратная последовательность результатов деления:

0₁₀=0_{10010010101001010101010100100100}

Окончательный ответ будет выглядеть так:

100100011010101010010010101001001010101010100110010101010000010101110010010001010100100101010100101010101000101010000100101001_{10010101010010}=0_{10010010101001010101010100100100}