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:
2567.5238 = 2 5 6 7. 5 2 3 = 2(=010) 5(=101) 6(=110) 7(=111). 5(=101) 2(=010) 3(=011) = 010101110111.1010100112
the Final answer: 2567.5238 = 10101110111.1010100112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
2∙83+5∙82+6∙81+7∙80+5∙8-1+2∙8-2+3∙8-3 = 2∙512+5∙64+6∙8+7∙1+5∙0.125+2∙0.015625+3∙0.001953125 = 1024+320+48+7+0.625+0.03125+0.005859375 = 1399.66210937510
got It: 2567.5238 =1399.66210937510
Translate the number 1399.66210937510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1399 | 2 | | | | | | | | | | |
-1398 | 699 | 2 | | | | | | | | | |
1 | -698 | 349 | 2 | | | | | | | | |
| 1 | -348 | 174 | 2 | | | | | | | |
| | 1 | -174 | 87 | 2 | | | | | | |
| | | 0 | -86 | 43 | 2 | | | | | |
| | | | 1 | -42 | 21 | 2 | | | | |
| | | | | 1 | -20 | 10 | 2 | | | |
| | | | | | 1 | -10 | 5 | 2 | | |
| | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | 0 | | |
 |
the Fractional part of the number is multiplied by the base of the new number system:
 |
0. | 662109375*2 |
1 | .32422*2 |
0 | .64844*2 |
1 | .29688*2 |
0 | .59375*2 |
1 | .1875*2 |
0 | .375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
1399.66210937510 = 10101110111.1010100112
the Final answer: 2567.5238 = 10101110111.1010100112