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:
756.438 = 7 5 6. 4 3 = 7(=111) 5(=101) 6(=110). 4(=100) 3(=011) = 111101110.1000112
the Final answer: 756.438 = 111101110.1000112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
7∙82+5∙81+6∙80+4∙8-1+3∙8-2 = 7∙64+5∙8+6∙1+4∙0.125+3∙0.015625 = 448+40+6+0.5+0.046875 = 494.54687510
got It: 756.438 =494.54687510
Translate the number 494.54687510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
494 | 2 | | | | | | | | |
-494 | 247 | 2 | | | | | | | |
0 | -246 | 123 | 2 | | | | | | |
| 1 | -122 | 61 | 2 | | | | | |
| | 1 | -60 | 30 | 2 | | | | |
| | | 1 | -30 | 15 | 2 | | | |
| | | | 0 | -14 | 7 | 2 | | |
| | | | | 1 | -6 | 3 | 2 | |
| | | | | | 1 | -2 | 1 | |
| | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 546875*2 |
1 | .09375*2 |
0 | .1875*2 |
0 | .375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
494.54687510 = 111101110.1000112
the Final answer: 756.438 = 111101110.1000112