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:
47.578 = 4 7. 5 7 = 4(=100) 7(=111). 5(=101) 7(=111) = 100111.1011112
answer: 47.578 = 100111.1011112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
4∙81+7∙80+5∙8-1+7∙8-2 = 4∙8+7∙1+5∙0.125+7∙0.015625 = 32+7+0.625+0.109375 = 39.73437510
got It: 47.578 =39.73437510
Translate the number 39.73437510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
39 | 2 | | | | | |
-38 | 19 | 2 | | | | |
1 | -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. | 734375*2 |
1 | .46875*2 |
0 | .9375*2 |
1 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
39.73437510 = 100111.1011112
answer: 47.578 = 100111.1011112