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:
5674.68 = 5 6 7 4. 6 = 5(=101) 6(=110) 7(=111) 4(=100). 6(=110) = 101110111100.1102
answer: 5674.68 = 101110111100.112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
5∙83+6∙82+7∙81+4∙80+6∙8-1 = 5∙512+6∙64+7∙8+4∙1+6∙0.125 = 2560+384+56+4+0.75 = 3004.7510
got It: 5674.68 =3004.7510
Translate the number 3004.7510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
3004 | 2 | | | | | | | | | | | |
-3004 | 1502 | 2 | | | | | | | | | | |
0 | -1502 | 751 | 2 | | | | | | | | | |
| 0 | -750 | 375 | 2 | | | | | | | | |
| | 1 | -374 | 187 | 2 | | | | | | | |
| | | 1 | -186 | 93 | 2 | | | | | | |
| | | | 1 | -92 | 46 | 2 | | | | | |
| | | | | 1 | -46 | 23 | 2 | | | | |
| | | | | | 0 | -22 | 11 | 2 | | | |
| | | | | | | 1 | -10 | 5 | 2 | | |
| | | | | | | | 1 | -4 | 2 | 2 | |
| | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
3004.7510 = 101110111100.112
answer: 5674.68 = 101110111100.112