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:
274.658 = 2 7 4. 6 5 = 2(=010) 7(=111) 4(=100). 6(=110) 5(=101) = 010111100.1101012
answer: 274.658 = 10111100.1101012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
2∙82+7∙81+4∙80+6∙8-1+5∙8-2 = 2∙64+7∙8+4∙1+6∙0.125+5∙0.015625 = 128+56+4+0.75+0.078125 = 188.82812510
got It: 274.658 =188.82812510
Translate the number 188.82812510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
188 | 2 | | | | | | | |
-188 | 94 | 2 | | | | | | |
0 | -94 | 47 | 2 | | | | | |
| 0 | -46 | 23 | 2 | | | | |
| | 1 | -22 | 11 | 2 | | | |
| | | 1 | -10 | 5 | 2 | | |
| | | | 1 | -4 | 2 | 2 | |
| | | | | 1 | -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:
188.82812510 = 10111100.1101012
answer: 274.658 = 10111100.1101012