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:
1234.568 = 1 2 3 4. 5 6 = 1(=001) 2(=010) 3(=011) 4(=100). 5(=101) 6(=110) = 001010011100.1011102
answer: 1234.568 = 1010011100.101112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙83+2∙82+3∙81+4∙80+5∙8-1+6∙8-2 = 1∙512+2∙64+3∙8+4∙1+5∙0.125+6∙0.015625 = 512+128+24+4+0.625+0.09375 = 668.7187510
got It: 1234.568 =668.7187510
Translate the number 668.7187510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
668 | 2 | | | | | | | | | |
-668 | 334 | 2 | | | | | | | | |
0 | -334 | 167 | 2 | | | | | | | |
| 0 | -166 | 83 | 2 | | | | | | |
| | 1 | -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. | 71875*2 |
1 | .4375*2 |
0 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
668.7187510 = 1010011100.101112
answer: 1234.568 = 1010011100.101112