Предмет: Информатика, автор: mstorozhenko7108

49^11+7^33-49=? Ответ записать в 7ричной системе счисления.

Ответы

Автор ответа: Enklgd01
0
Сначала немножко упростим формулу
49^11 = (7^2)^11 = 7^22
т.о. общая формула получается 7^22+7^33-7^2
Будем считать сразу в 7ричной системе:
число (система счисления)^степень = это 1(и столько нулей, какая степень), и это число уже в нужной системе, например:
10^0=1 (0 нулей);10^1 = 10 (1 ноль);10^2=100 (2 нуля) и т.д.
это правило действует во всех системах счисления
7^22=10000000000000000000000 (22 нуля, число уже в 7ричной системе)
7^33=1000000000000000000000000000000000 (33 нуля, число уже в 7ричной системе)
7^2=100 (2 нуля, число уже в 7ричной системе)
10000000000000000000000 + 1000000000000000000000000000000000 - 100
(считать проще в столбик, сначала сложение)
1000000000000000000000000000000000 +
           10000000000000000000000 =
1000000000010000000000000000000000
(вычитать тоже проще в столбик, только у старшего разряда при вычитании не 9, как в 10тичной системе, а 6)
1000000000010000000000000000000000 -
                               100
1000000000006666666666666666666600

Заметка 1: если пытаться считать "в лоб", то получаются числа с 27 цифрами, которые потом переводить - без соответствующего калькулятора не справиться
Заметка 2: нет возможности поставить у вычислений в столбец моноширинный шрифт, чтобы получилось красиво.
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