This transfer is possible in two ways: direct transfer and using the decimal system.
first, let\'s make a direct transfer.
let\'s do a direct translation from octal to binary like this:
10110110.10108 = 1 0 1 1 0 1 1 0. 1 0 1 0 = 1(=001) 0(=000) 1(=001) 1(=001) 0(=000) 1(=001) 1(=001) 0(=000). 1(=001) 0(=000) 1(=001) 0(=000) = 001000001001000001001000.0010000010002
answer: 10110110.10108 = 1000001001000001001000.0010000012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙87+0∙86+1∙85+1∙84+0∙83+1∙82+1∙81+0∙80+1∙8-1+0∙8-2+1∙8-3+0∙8-4 = 1∙2097152+0∙262144+1∙32768+1∙4096+0∙512+1∙64+1∙8+0∙1+1∙0.125+0∙0.015625+1∙0.001953125+0∙0.000244140625 = 2097152+0+32768+4096+0+64+8+0+0.125+0+0.001953125+0 = 2134088.12695312510
got It: 10110110.10108 =2134088.12695312510
Translate the number 2134088.12695312510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
2134088 | 2 | | | | | | | | | | | | | | | | | | | | | |
-2134088 | 1067044 | 2 | | | | | | | | | | | | | | | | | | | | |
0 | -1067044 | 533522 | 2 | | | | | | | | | | | | | | | | | | | |
| 0 | -533522 | 266761 | 2 | | | | | | | | | | | | | | | | | | |
| | 0 | -266760 | 133380 | 2 | | | | | | | | | | | | | | | | | |
| | | 1 | -133380 | 66690 | 2 | | | | | | | | | | | | | | | | |
| | | | 0 | -66690 | 33345 | 2 | | | | | | | | | | | | | | | |
| | | | | 0 | -33344 | 16672 | 2 | | | | | | | | | | | | | | |
| | | | | | 1 | -16672 | 8336 | 2 | | | | | | | | | | | | | |
| | | | | | | 0 | -8336 | 4168 | 2 | | | | | | | | | | | | |
| | | | | | | | 0 | -4168 | 2084 | 2 | | | | | | | | | | | |
| | | | | | | | | 0 | -2084 | 1042 | 2 | | | | | | | | | | |
| | | | | | | | | | 0 | -1042 | 521 | 2 | | | | | | | | | |
| | | | | | | | | | | 0 | -520 | 260 | 2 | | | | | | | | |
| | | | | | | | | | | | 1 | -260 | 130 | 2 | | | | | | | |
| | | | | | | | | | | | | 0 | -130 | 65 | 2 | | | | | | |
| | | | | | | | | | | | | | 0 | -64 | 32 | 2 | | | | | |
| | | | | | | | | | | | | | | 1 | -32 | 16 | 2 | | | | |
| | | | | | | | | | | | | | | | 0 | -16 | 8 | 2 | | | |
| | | | | | | | | | | | | | | | | 0 | -8 | 4 | 2 | | |
| | | | | | | | | | | | | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | | | | | | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | | | | | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 126953125*2 |
0 | .25391*2 |
0 | .50781*2 |
1 | .01563*2 |
0 | .03125*2 |
0 | .0625*2 |
0 | .125*2 |
0 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
2134088.12695312510 = 1000001001000001001000.0010000012
answer: 10110110.10108 = 1000001001000001001000.0010000012