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:
115.658 = 1 1 5. 6 5 = 1(=001) 1(=001) 5(=101). 6(=110) 5(=101) = 001001101.1101012
answer: 115.658 = 1001101.1101012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙82+1∙81+5∙80+6∙8-1+5∙8-2 = 1∙64+1∙8+5∙1+6∙0.125+5∙0.015625 = 64+8+5+0.75+0.078125 = 77.82812510
got It: 115.658 =77.82812510
Translate the number 77.82812510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
77 | 2 | | | | | | |
-76 | 38 | 2 | | | | | |
1 | -38 | 19 | 2 | | | | |
| 0 | -18 | 9 | 2 | | | |
| | 1 | -8 | 4 | 2 | | |
| | | 1 | -4 | 2 | 2 | |
| | | | 0 | -2 | 1 | |
| | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 828125*2 |
1 | .65625*2 |
1 | .3125*2 |
0 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
77.82812510 = 1001101.1101012
answer: 115.658 = 1001101.1101012