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:
524.448 = 5 2 4. 4 4 = 5(=101) 2(=010) 4(=100). 4(=100) 4(=100) = 101010100.1001002
answer: 524.448 = 101010100.10012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
5∙82+2∙81+4∙80+4∙8-1+4∙8-2 = 5∙64+2∙8+4∙1+4∙0.125+4∙0.015625 = 320+16+4+0.5+0.0625 = 340.562510
got It: 524.448 =340.562510
Translate the number 340.562510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
340 | 2 | | | | | | | | |
-340 | 170 | 2 | | | | | | | |
0 | -170 | 85 | 2 | | | | | | |
| 0 | -84 | 42 | 2 | | | | | |
| | 1 | -42 | 21 | 2 | | | | |
| | | 0 | -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. | 5625*2 |
1 | .125*2 |
0 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
340.562510 = 101010100.10012
answer: 524.448 = 101010100.10012