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:
11010.10118 = 1 1 0 1 0. 1 0 1 1 = 1(=001) 1(=001) 0(=000) 1(=001) 0(=000). 1(=001) 0(=000) 1(=001) 1(=001) = 001001000001000.0010000010012
answer: 11010.10118 = 1001000001000.0010000010012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙84+1∙83+0∙82+1∙81+0∙80+1∙8-1+0∙8-2+1∙8-3+1∙8-4 = 1∙4096+1∙512+0∙64+1∙8+0∙1+1∙0.125+0∙0.015625+1∙0.001953125+1∙0.000244140625 = 4096+512+0+8+0+0.125+0+0.001953125+0.000244140625 = 4616.12719726562510
got It: 11010.10118 =4616.12719726562510
Translate the number 4616.12719726562510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
4616 | 2 | | | | | | | | | | | | |
-4616 | 2308 | 2 | | | | | | | | | | | |
0 | -2308 | 1154 | 2 | | | | | | | | | | |
| 0 | -1154 | 577 | 2 | | | | | | | | | |
| | 0 | -576 | 288 | 2 | | | | | | | | |
| | | 1 | -288 | 144 | 2 | | | | | | | |
| | | | 0 | -144 | 72 | 2 | | | | | | |
| | | | | 0 | -72 | 36 | 2 | | | | | |
| | | | | | 0 | -36 | 18 | 2 | | | | |
| | | | | | | 0 | -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. | 127197265625*2 |
0 | .25439*2 |
0 | .50879*2 |
1 | .01758*2 |
0 | .03516*2 |
0 | .07031*2 |
0 | .14063*2 |
0 | .28125*2 |
0 | .5625*2 |
1 | .125*2 |
0 | .25*2 |
the result of the conversion was:
4616.12719726562510 = 1001000001000.00100000102
answer: 11010.10118 = 1001000001000.00100000102