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:
450.78 = 4 5 0. 7 = 4(=100) 5(=101) 0(=000). 7(=111) = 100101000.1112
answer: 450.78 = 100101000.1112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
4∙82+5∙81+0∙80+7∙8-1 = 4∙64+5∙8+0∙1+7∙0.125 = 256+40+0+0.875 = 296.87510
got It: 450.78 =296.87510
Translate the number 296.87510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
296 | 2 | | | | | | | | |
-296 | 148 | 2 | | | | | | | |
0 | -148 | 74 | 2 | | | | | | |
| 0 | -74 | 37 | 2 | | | | | |
| | 0 | -36 | 18 | 2 | | | | |
| | | 1 | -18 | 9 | 2 | | | |
| | | | 0 | -8 | 4 | 2 | | |
| | | | | 1 | -4 | 2 | 2 | |
| | | | | | 0 | -2 | 1 | |
| | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
296.87510 = 100101000.1112
answer: 450.78 = 100101000.1112