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:
156.728 = 1 5 6. 7 2 = 1(=001) 5(=101) 6(=110). 7(=111) 2(=010) = 001101110.1110102
answer: 156.728 = 1101110.111012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙82+5∙81+6∙80+7∙8-1+2∙8-2 = 1∙64+5∙8+6∙1+7∙0.125+2∙0.015625 = 64+40+6+0.875+0.03125 = 110.9062510
got It: 156.728 =110.9062510
Translate the number 110.9062510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
110 | 2 | | | | | | |
-110 | 55 | 2 | | | | | |
0 | -54 | 27 | 2 | | | | |
| 1 | -26 | 13 | 2 | | | |
| | 1 | -12 | 6 | 2 | | |
| | | 1 | -6 | 3 | 2 | |
| | | | 0 | -2 | 1 | |
| | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 90625*2 |
1 | .8125*2 |
1 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
110.9062510 = 1101110.111012
answer: 156.728 = 1101110.111012