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:
123.458 = 1 2 3. 4 5 = 1(=001) 2(=010) 3(=011). 4(=100) 5(=101) = 001010011.1001012
answer: 123.458 = 1010011.1001012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙82+2∙81+3∙80+4∙8-1+5∙8-2 = 1∙64+2∙8+3∙1+4∙0.125+5∙0.015625 = 64+16+3+0.5+0.078125 = 83.57812510
got It: 123.458 =83.57812510
Translate the number 83.57812510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
83 | 2 | | | | | | |
-82 | 41 | 2 | | | | | |
1 | -40 | 20 | 2 | | | | |
| 1 | -20 | 10 | 2 | | | |
| | 0 | -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. | 578125*2 |
1 | .15625*2 |
0 | .3125*2 |
0 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
83.57812510 = 1010011.1001012
answer: 123.458 = 1010011.1001012