Мы определили что два или более чисел находятся в разных системах счисления.
Для правильного выполнения всех арифметических операций необходимо
перевести все числа в какую-нибудь одну систему счисления.
Вы выбрали двоичную систему счисления поэтому в нее осуществим перевод всех чисел.
1) Число 111011000.101
2 уже находится в нужной СС.
2)
Переведем число 1101100011.10116Для этого переведем его сначала в десятичную вот так:
1101100011.101
16 = 1∙16
9+1∙16
8+0∙16
7+1∙16
6+1∙16
5+0∙16
4+0∙16
3+0∙16
2+1∙16
1+1∙16
0+1∙16
-1+0∙16
-2+1∙16
-3 = 68719476736+4294967296+0+16777216+1048576+0+0+0+16+1+0.0625+0+0.000244140625 = 73032269841.063
10Целая часть находится делением на основание новой:
73032269841 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
-73032269840 | 36516134920 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
1 | -36516134920 | 18258067460 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| 0 | -18258067460 | 9129033730 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | 0 | -9129033730 | 4564516865 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | 0 | -4564516864 | 2282258432 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | 1 | -2282258432 | 1141129216 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | 0 | -1141129216 | 570564608 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | 0 | -570564608 | 285282304 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | 0 | -285282304 | 142641152 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | 0 | -142641152 | 71320576 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | 0 | -71320576 | 35660288 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | 0 | -35660288 | 17830144 | 2 | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | 0 | -17830144 | 8915072 | 2 | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | 0 | -8915072 | 4457536 | 2 | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | 0 | -4457536 | 2228768 | 2 | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | 0 | -2228768 | 1114384 | 2 | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | 0 | -1114384 | 557192 | 2 | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | 0 | -557192 | 278596 | 2 | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | 0 | -278596 | 139298 | 2 | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | 0 | -139298 | 69649 | 2 | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | 0 | -69648 | 34824 | 2 | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | 1 | -34824 | 17412 | 2 | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | 0 | -17412 | 8706 | 2 | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | 0 | -8706 | 4353 | 2 | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | 0 | -4352 | 2176 | 2 | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | 1 | -2176 | 1088 | 2 | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | 0 | -1088 | 544 | 2 | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -544 | 272 | 2 | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -272 | 136 | 2 | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -136 | 68 | 2 | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -68 | 34 | 2 | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -34 | 17 | 2 | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -16 | 8 | 2 | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -8 | 4 | 2 | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | | |
|
Дробная часть находится умножением на основание новой:
|
0 | .063 |
. | 2 |
0 | 126 |
| 2 |
0 | 252 |
| 2 |
0 | 504 |
| 2 |
1 | 008 |
| 2 |
0 | 016 |
| 2 |
0 | 032 |
| 2 |
0 | 064 |
| 2 |
0 | 128 |
| 2 |
0 | 256 |
| 2 |
0 | 512 |
| 2 |
1 | 024 |
| 2 |
Результат перевода:
1101100011.10116 = 1000100000001000100000000000000010001.000100000002В результате преобразований получили выражение:
111011000.1012+1000100000001000100000000000000010001.000100000002 В полученном выражении все числа находятся в двоичной системе счисления. Поэтому все расчеты будем выполнять в ней.
1)
Выполним сложение 111011000.1012+1000100000001000100000000000000010001.000100000002 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
+ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | . | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | . | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | . | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Получилось: 111011000.101
2+1000100000001000100000000000000010001.00010000000
2 = 1000100000001000100000000000111101001.1011
2 Вы пожелали видеть ответ в шестнадцатеричной системе счисления
Переведем его сначала в десятичную вот так:
1000100000001000100000000000111101001.1011
2 = 1∙2
36+0∙2
35+0∙2
34+0∙2
33+1∙2
32+0∙2
31+0∙2
30+0∙2
29+0∙2
28+0∙2
27+0∙2
26+0∙2
25+1∙2
24+0∙2
23+0∙2
22+0∙2
21+1∙2
20+0∙2
19+0∙2
18+0∙2
17+0∙2
16+0∙2
15+0∙2
14+0∙2
13+0∙2
12+0∙2
11+0∙2
10+0∙2
9+1∙2
8+1∙2
7+1∙2
6+1∙2
5+0∙2
4+1∙2
3+0∙2
2+0∙2
1+1∙2
0+1∙2
-1+0∙2
-2+1∙2
-3+1∙2
-4 = 68719476736+0+0+0+4294967296+0+0+0+0+0+0+0+16777216+0+0+0+1048576+0+0+0+0+0+0+0+0+0+0+0+256+128+64+32+0+8+0+0+1+0.5+0+0.125+0.0625 = 73032270313.688
10Резульат перевода:
1000100000001000100000000000111101001.1011
2 = 73032270313.688
10Теперь переведем его в 16 -ричную:
Целая часть находится делением на основание новой:
73032270313 | 16 | | | | | | | | | |
-73032270304 | 4564516894 | 16 | | | | | | | | |
9 | -4564516880 | 285282305 | 16 | | | | | | | |
| 14=E | -285282304 | 17830144 | 16 | | | | | | |
| | 1 | -17830144 | 1114384 | 16 | | | | | |
| | | 0 | -1114384 | 69649 | 16 | | | | |
| | | | 0 | -69648 | 4353 | 16 | | | |
| | | | | 1 | -4352 | 272 | 16 | | |
| | | | | | 1 | -272 | 17 | 16 | |
| | | | | | | 0 | -16 | 1 | |
| | | | | | | | 1 | | |
|
Дробная часть находится умножением на основание новой:
|
0 | .688 |
. | 16 |
11=B | 008 |
| 16 |
0 | 128 |
| 16 |
2 | 048 |
| 16 |
0 | 768 |
| 16 |
12=C | 288 |
| 16 |
4 | 608 |
| 16 |
9 | 728 |
| 16 |
11=B | 648 |
| 16 |
10=A | 368 |
| 16 |
5 | 88794 |
| 16 |
14=E | 20703 |
| 16 |
Окончательный ответ:11011001E9.B16