Перевести число 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 из 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999-ой системы в двоичную
Задача: перевести число 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 из 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999-ой в двоичную систему счисления.
Для перевода 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 из 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999-ой в двоичную систему счисления, воспользуемся следующим алгоритмом:
- Переведем число 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 из 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999-ой системы в десятичную;
- Полученное число переведём из десятичной системы в двоичную;
Решение:
1. Для перевода числа 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 в десятичную систему воспользуемся формулой:
An = an-1 ∙ qn-1 + an-2 ∙ qn-2 + ∙∙∙ + a0 ∙ q0
Отсюда:
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999=9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999994 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999992 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999989 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999988 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999987 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999986 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999985 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999984 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999983 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999982 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999981 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999980 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999979 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999978 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999977 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999976 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999975 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999974 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999973 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999972 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999971 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999970 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999969 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999968 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999967 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999966 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999965 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999964 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999963 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999962 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999961 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999960 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999959 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999958 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999957 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999956 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999955 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999954 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999953 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999952 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999951 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999950 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999949 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999948 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999947 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999946 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999945 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999944 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999943 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999942 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999941 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999940 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999939 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999938 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999937 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999936 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999935 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999934 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999933 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999932 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999931 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999930 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999929 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999928 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999927 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999926 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999925 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999924 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999923 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999922 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999921 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999920 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999919 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999918 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999917 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999916 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999915 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999914 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999913 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999912 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999911 + 9 ∙ 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999910 + 9 ∙ 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 + 9 ∙ 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998 + 9 ∙ 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 + 9 ∙ 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996 + 9 ∙ 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999995 + 9 ∙ 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999994 + 9 ∙ 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 + 9 ∙ 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999992 + 9 ∙ 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 + 9 ∙ 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990 = 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ INF + 9 ∙ 1.0E+212 + 9 ∙ 1.0E+106 + 9 ∙ 1 = INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + 9.0E+212 + 9.0E+106 + 9 = INF10
Таким образом:
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 = INF10
2. Полученное число INF переведем из десятичной системы счисления в двоичную. Для этого, осуществим последовательное деление на 2, до тех пор пока остаток не будет меньше чем 2.
| 0 | |
Полученные остатки записываем в обратном порядке, таким образом:
010=02
Ответ: 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 = 02.
Смотрите также:
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