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 десятичную систему счисления поэтому в нее осуществим перевод всех чисел.
1)
Переведем число 11111111111111010000100001001110111111111111111111111111111111112Для этого переведем его сначала в десятичную вот так:
1111111111111101000010000100111011111111111111111111111111111111
2 = 1∙2
63+1∙2
62+1∙2
61+1∙2
60+1∙2
59+1∙2
58+1∙2
57+1∙2
56+1∙2
55+1∙2
54+1∙2
53+1∙2
52+1∙2
51+1∙2
50+0∙2
49+1∙2
48+0∙2
47+0∙2
46+0∙2
45+0∙2
44+1∙2
43+0∙2
42+0∙2
41+0∙2
40+0∙2
39+1∙2
38+0∙2
37+0∙2
36+1∙2
35+1∙2
34+1∙2
33+0∙2
32+1∙2
31+1∙2
30+1∙2
29+1∙2
28+1∙2
27+1∙2
26+1∙2
25+1∙2
24+1∙2
23+1∙2
22+1∙2
21+1∙2
20+1∙2
19+1∙2
18+1∙2
17+1∙2
16+1∙2
15+1∙2
14+1∙2
13+1∙2
12+1∙2
11+1∙2
10+1∙2
9+1∙2
8+1∙2
7+1∙2
6+1∙2
5+1∙2
4+1∙2
3+1∙2
2+1∙2
1+1∙2
0 = 9.2233720368548E+18+4611686018427387904+2305843009213693952+1152921504606846976+576460752303423488+288230376151711744+144115188075855872+72057594037927936+36028797018963968+18014398509481984+9007199254740992+4503599627370496+2251799813685248+1125899906842624+0+281474976710656+0+0+0+0+8796093022208+0+0+0+0+274877906944+0+0+34359738368+17179869184+8589934592+0+2147483648+1073741824+536870912+268435456+134217728+67108864+33554432+16777216+8388608+4194304+2097152+1048576+524288+262144+131072+65536+32768+16384+8192+4096+2048+1024+512+256+128+64+32+16+8+4+2+1 = 1.8445908784175E+19
10Целая часть находится делением на основание новой:
-835289534693376
10 = -835289534693376
10Дробная часть находится умножением на основание новой:
|
0 | .8445908784175E+19 |
. | 10 |
-7774632526797766656 | 445908784175E+19 |
| 10 |
0 | 2233720368548E+20 |
| 10 |
0 | 2233720368548E+21 |
| 10 |
0 | 2233720368548E+22 |
| 10 |
0 | 2233720368548E+23 |
| 10 |
0 | 2233720368548E+24 |
| 10 |
0 | 2233720368548E+25 |
| 10 |
0 | 2233720368548E+26 |
| 10 |
0 | 2233720368548E+27 |
| 10 |
0 | 2233720368548E+28 |
| 10 |
0 | 2233720368548E+29 |
| 10 |
Результат перевода:
11111111111111010000100001001110111111111111111111111111111111112 = 835289534693376.0000000000010 2)
Переведем число 450359962737049616Для этого переведем его сначала в десятичную вот так:
4503599627370496
16 = 4∙16
15+5∙16
14+0∙16
13+3∙16
12+5∙16
11+9∙16
10+9∙16
9+6∙16
8+2∙16
7+7∙16
6+3∙16
5+7∙16
4+0∙16
3+4∙16
2+9∙16
1+6∙16
0 = 4611686018427387904+360287970189639680+0+844424930131968+87960930222080+9895604649984+618475290624+25769803776+536870912+117440512+3145728+458752+0+1024+144+6 = 4972916914985043094
10Целая часть находится делением на основание новой:
4972916914985043094 | 10 | | | | | | | | | | | | | | | | | | |
-4972916914985043200 | 497291691498504320 | 10 | | | | | | | | | | | | | | | | | |
4 | -497291691498504320 | 49729169149850432 | 10 | | | | | | | | | | | | | | | | |
| 0 | -49729169149850430 | 4972916914985043 | 10 | | | | | | | | | | | | | | | |
| | 2 | -4972916914985040 | 497291691498504 | 10 | | | | | | | | | | | | | | |
| | | 3 | -497291691498500 | 49729169149850 | 10 | | | | | | | | | | | | | |
| | | | 4 | -49729169149850 | 4972916914985 | 10 | | | | | | | | | | | | |
| | | | | 0 | -4972916914980 | 497291691498 | 10 | | | | | | | | | | | |
| | | | | | 5 | -497291691490 | 49729169149 | 10 | | | | | | | | | | |
| | | | | | | 8 | -49729169140 | 4972916914 | 10 | | | | | | | | | |
| | | | | | | | 9 | -4972916910 | 497291691 | 10 | | | | | | | | |
| | | | | | | | | 4 | -497291690 | 49729169 | 10 | | | | | | | |
| | | | | | | | | | 1 | -49729160 | 4972916 | 10 | | | | | | |
| | | | | | | | | | | 9 | -4972910 | 497291 | 10 | | | | | |
| | | | | | | | | | | | 6 | -497290 | 49729 | 10 | | | | |
| | | | | | | | | | | | | 1 | -49720 | 4972 | 10 | | | |
| | | | | | | | | | | | | | 9 | -4970 | 497 | 10 | | |
| | | | | | | | | | | | | | | 2 | -490 | 49 | 10 | |
| | | | | | | | | | | | | | | | 7 | -40 | 4 | |
| | | | | | | | | | | | | | | | | 9 | | |
|
Результат перевода:
450359962737049616 = 497291691498504309410В результате преобразований получили выражение:
835289534693376.0000000000010*497291691498504309410 В полученном выражении все числа находятся в десятичной системе счисления. Поэтому все расчеты будем выполнять в ней.
1)
Выполним умножение 835289534693376.0000000000010*497291691498504309410x | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 8 | 3 | 5 | 2 | 8 | 9 | 5 | 3 | 4 | 6 | 9 | 3 | 3 | 7 | 6 | . | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| | | | | | | | | | | | | | | | | | | | | | | | | | | 4 | 9 | 7 | 2 | 9 | 1 | 6 | 9 | 1 | 4 | 9 | 8 | 5 | 0 | 4 | 3 | 0 | 9 | 4 | . | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
+ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | 3 | 3 | 4 | 1 | 1 | 5 | 8 | 1 | 3 | 8 | 7 | 7 | 3 | 5 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | 7 | 5 | 1 | 7 | 6 | 0 | 5 | 8 | 1 | 2 | 2 | 4 | 0 | 3 | 8 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | 2 | 5 | 0 | 5 | 8 | 6 | 8 | 6 | 0 | 4 | 0 | 8 | 0 | 1 | 2 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | 3 | 3 | 4 | 1 | 1 | 5 | 8 | 1 | 3 | 8 | 7 | 7 | 3 | 5 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | 4 | 1 | 7 | 6 | 4 | 4 | 7 | 6 | 7 | 3 | 4 | 6 | 6 | 8 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | 6 | 6 | 8 | 2 | 3 | 1 | 6 | 2 | 7 | 7 | 5 | 4 | 7 | 0 | 0 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | 7 | 5 | 1 | 7 | 6 | 0 | 5 | 8 | 1 | 2 | 2 | 4 | 0 | 3 | 8 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | 3 | 3 | 4 | 1 | 1 | 5 | 8 | 1 | 3 | 8 | 7 | 7 | 3 | 5 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | 8 | 3 | 5 | 2 | 8 | 9 | 5 | 3 | 4 | 6 | 9 | 3 | 3 | 7 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | 7 | 5 | 1 | 7 | 6 | 0 | 5 | 8 | 1 | 2 | 2 | 4 | 0 | 3 | 8 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | 5 | 0 | 1 | 1 | 7 | 3 | 7 | 2 | 0 | 8 | 1 | 6 | 0 | 2 | 5 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | 8 | 3 | 5 | 2 | 8 | 9 | 5 | 3 | 4 | 6 | 9 | 3 | 3 | 7 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | 7 | 5 | 1 | 7 | 6 | 0 | 5 | 8 | 1 | 2 | 2 | 4 | 0 | 3 | 8 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | 1 | 6 | 7 | 0 | 5 | 7 | 9 | 0 | 6 | 9 | 3 | 8 | 6 | 7 | 5 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | 5 | 8 | 4 | 7 | 0 | 2 | 6 | 7 | 4 | 2 | 8 | 5 | 3 | 6 | 3 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | 7 | 5 | 1 | 7 | 6 | 0 | 5 | 8 | 1 | 2 | 2 | 4 | 0 | 3 | 8 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | 3 | 3 | 4 | 1 | 1 | 5 | 8 | 1 | 3 | 8 | 7 | 7 | 3 | 5 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | 4 | 1 | 5 | 3 | 8 | 2 | 5 | 4 | 5 | 5 | 9 | 8 | 6 | 6 | 7 | 5 | 5 | 0 | 1 | 8 | 0 | 1 | 8 | 4 | 7 | 4 | 3 | 6 | 3 | 4 | 5 | 3 | 4 | 4. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Получилось: 835289534693376.00000000000
10*4972916914985043094
10 = 4153825455986675501801847436345344.0000000000000000000000
10 Вы пожелали видеть ответ в шестнадцатеричной системе счисления
Целая часть находится делением на основание новой:
9223372036854775807 | 16 | | | | | | | | | | | | | | | |
-9223372036854775808 | 576460752303423488 | 16 | | | | | | | | | | | | | | |
15=F | -576460752303423488 | 36028797018963968 | 16 | | | | | | | | | | | | | |
| 0 | -36028797018963968 | 2251799813685248 | 16 | | | | | | | | | | | | |
| | 0 | -2251799813685248 | 140737488355328 | 16 | | | | | | | | | | | |
| | | 0 | -140737488355328 | 8796093022208 | 16 | | | | | | | | | | |
| | | | 0 | -8796093022208 | 549755813888 | 16 | | | | | | | | | |
| | | | | 0 | -549755813888 | 34359738368 | 16 | | | | | | | | |
| | | | | | 0 | -34359738368 | 2147483648 | 16 | | | | | | | |
| | | | | | | 0 | -2147483648 | 134217728 | 16 | | | | | | |
| | | | | | | | 0 | -134217728 | 8388608 | 16 | | | | | |
| | | | | | | | | 0 | -8388608 | 524288 | 16 | | | | |
| | | | | | | | | | 0 | -524288 | 32768 | 16 | | | |
| | | | | | | | | | | 0 | -32768 | 2048 | 16 | | |
| | | | | | | | | | | | 0 | -2048 | 128 | 16 | |
| | | | | | | | | | | | | 0 | -128 | 8 | |
| | | | | | | | | | | | | | 0 | | |
|
Дробная часть находится умножением на основание новой:
|
0 | .0000000000000000000000 |
. | 16 |
Окончательный ответ:7FFFFFFFFFFFFFFF.-9223372036854775808000000000016