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:
3567.258 = 3 5 6 7. 2 5 = 3(=011) 5(=101) 6(=110) 7(=111). 2(=010) 5(=101) = 011101110111.0101012
answer: 3567.258 = 11101110111.0101012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
3∙83+5∙82+6∙81+7∙80+2∙8-1+5∙8-2 = 3∙512+5∙64+6∙8+7∙1+2∙0.125+5∙0.015625 = 1536+320+48+7+0.25+0.078125 = 1911.32812510
got It: 3567.258 =1911.32812510
Translate the number 1911.32812510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1911 | 2 | | | | | | | | | | |
-1910 | 955 | 2 | | | | | | | | | |
1 | -954 | 477 | 2 | | | | | | | | |
| 1 | -476 | 238 | 2 | | | | | | | |
| | 1 | -238 | 119 | 2 | | | | | | |
| | | 0 | -118 | 59 | 2 | | | | | |
| | | | 1 | -58 | 29 | 2 | | | | |
| | | | | 1 | -28 | 14 | 2 | | | |
| | | | | | 1 | -14 | 7 | 2 | | |
| | | | | | | 0 | -6 | 3 | 2 | |
| | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 328125*2 |
0 | .65625*2 |
1 | .3125*2 |
0 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
1911.32812510 = 11101110111.0101012
answer: 3567.258 = 11101110111.0101012