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:
1053.278 = 1 0 5 3. 2 7 = 1(=001) 0(=000) 5(=101) 3(=011). 2(=010) 7(=111) = 001000101011.0101112
answer: 1053.278 = 1000101011.0101112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙83+0∙82+5∙81+3∙80+2∙8-1+7∙8-2 = 1∙512+0∙64+5∙8+3∙1+2∙0.125+7∙0.015625 = 512+0+40+3+0.25+0.109375 = 555.35937510
got It: 1053.278 =555.35937510
Translate the number 555.35937510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
555 | 2 | | | | | | | | | |
-554 | 277 | 2 | | | | | | | | |
1 | -276 | 138 | 2 | | | | | | | |
| 1 | -138 | 69 | 2 | | | | | | |
| | 0 | -68 | 34 | 2 | | | | | |
| | | 1 | -34 | 17 | 2 | | | | |
| | | | 0 | -16 | 8 | 2 | | | |
| | | | | 1 | -8 | 4 | 2 | | |
| | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | 0 | -2 | 1 | |
| | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 359375*2 |
0 | .71875*2 |
1 | .4375*2 |
0 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
555.35937510 = 1000101011.0101112
answer: 1053.278 = 1000101011.0101112