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:
716.678 = 7 1 6. 6 7 = 7(=111) 1(=001) 6(=110). 6(=110) 7(=111) = 111001110.1101112
answer: 716.678 = 111001110.1101112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
7∙82+1∙81+6∙80+6∙8-1+7∙8-2 = 7∙64+1∙8+6∙1+6∙0.125+7∙0.015625 = 448+8+6+0.75+0.109375 = 462.85937510
got It: 716.678 =462.85937510
Translate the number 462.85937510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
462 | 2 | | | | | | | | |
-462 | 231 | 2 | | | | | | | |
0 | -230 | 115 | 2 | | | | | | |
| 1 | -114 | 57 | 2 | | | | | |
| | 1 | -56 | 28 | 2 | | | | |
| | | 1 | -28 | 14 | 2 | | | |
| | | | 0 | -14 | 7 | 2 | | |
| | | | | 0 | -6 | 3 | 2 | |
| | | | | | 1 | -2 | 1 | |
| | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 859375*2 |
1 | .71875*2 |
1 | .4375*2 |
0 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
462.85937510 = 111001110.1101112
answer: 716.678 = 111001110.1101112