Для перевода числа 11101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001 из 11101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001-ой в 11101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001-ую систему счисления, необходимо сначала перевести его в десятичную систему, а полученное число в 11101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001-ую. Для перевода 11101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001-ого числа 11101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001 в десятичное необходимо записать его в виде многочлена, состоящего из произведений цифр вида:
A11101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001 = an-1 ∙ 11101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001n-1 + an-2 ∙ 11101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001n-2 + ∙∙∙ + a0 ∙ 111010001110010011101000111100101110010110000011101101111000001000001111010111110011111010010
В результате преобразований получим:
1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100111101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001=1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100191 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100190 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100189 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100188 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100187 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100186 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100185 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100184 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100183 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100182 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100181 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100180 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100179 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100178 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100177 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100176 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100175 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100174 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100173 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100172 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100171 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100170 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100169 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100168 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100167 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100166 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100165 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100164 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100163 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100162 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100161 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100160 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100159 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100158 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100157 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100156 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100155 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100154 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100153 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100152 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100151 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100150 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100149 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100148 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100147 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100146 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100145 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100144 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100143 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100142 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100141 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100140 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100139 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100138 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100137 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100136 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100135 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100134 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100133 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100132 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100131 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100130 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100129 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100128 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100127 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100126 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100125 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100124 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100123 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100122 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100121 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100120 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100119 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100118 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100117 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100116 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100115 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100114 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100113 + 1 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100112 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100111 + 0 ∙ 1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100110 + 1 ∙ 111010001110010011101000111100101110010110000011101101111000001000001111010111110011111010019 + 1 ∙ 111010001110010011101000111100101110010110000011101101111000001000001111010111110011111010018 + 1 ∙ 111010001110010011101000111100101110010110000011101101111000001000001111010111110011111010017 + 1 ∙ 111010001110010011101000111100101110010110000011101101111000001000001111010111110011111010016 + 1 ∙ 111010001110010011101000111100101110010110000011101101111000001000001111010111110011111010015 + 0 ∙ 111010001110010011101000111100101110010110000011101101111000001000001111010111110011111010014 + 1 ∙ 111010001110010011101000111100101110010110000011101101111000001000001111010111110011111010013 + 0 ∙ 111010001110010011101000111100101110010110000011101101111000001000001111010111110011111010012 + 0 ∙ 111010001110010011101000111100101110010110000011101101111000001000001111010111110011111010011 + 1 ∙ 111010001110010011101000111100101110010110000011101101111000001000001111010111110011111010010 = 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 0 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 1 ∙ INF + 0 ∙ INF + 1 ∙ 1.3680007043377E+273 + 0 ∙ 1.2323220346444E+182 + 0 ∙ 1.1101000111001E+91 + 1 ∙ 1 = INF + INF + INF + NAN + INF + NAN + NAN + NAN + INF + INF + INF + NAN + NAN + INF + NAN + NAN + INF + INF + INF + NAN + INF + NAN + NAN + NAN + INF + INF + INF + INF + NAN + NAN + INF + NAN + INF + INF + INF + NAN + NAN + INF + NAN + INF + INF + NAN + NAN + NAN + NAN + NAN + INF + INF + INF + NAN + INF + INF + NAN + INF + INF + INF + INF + NAN + NAN + NAN + NAN + NAN + INF + NAN + NAN + NAN + NAN + NAN + INF + INF + INF + INF + NAN + INF + NAN + INF + INF + INF + INF + INF + NAN + NAN + INF + INF + INF + INF + INF + NAN + 1.3680007043377E+273 + 0 + 0 + 1 = NAN10
Таким образом:
1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100111101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001 = NAN10.
Для перевода десятичного числа NAN в 11101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001-ую систему счисления, необходимо его последовательно делить на 11101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001 до тех пор, пока остаток не станет меньше чем 11101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001.
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Ответом будет являться обратная последовательность результатов деления:
010=011101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001
Окончательный ответ будет выглядеть так:
1110100011100100111010001111001011100101100000111011011110000010000011110101111100111110100111101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001=011101000111001001110100011110010111001011000001110110111100000100000111101011111001111101001