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:
13705.2078 = 1 3 7 0 5. 2 0 7 = 1(=001) 3(=011) 7(=111) 0(=000) 5(=101). 2(=010) 0(=000) 7(=111) = 001011111000101.0100001112
answer: 13705.2078 = 1011111000101.0100001112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙84+3∙83+7∙82+0∙81+5∙80+2∙8-1+0∙8-2+7∙8-3 = 1∙4096+3∙512+7∙64+0∙8+5∙1+2∙0.125+0∙0.015625+7∙0.001953125 = 4096+1536+448+0+5+0.25+0+0.013671875 = 6085.26367187510
got It: 13705.2078 =6085.26367187510
Translate the number 6085.26367187510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
6085 | 2 | | | | | | | | | | | | |
-6084 | 3042 | 2 | | | | | | | | | | | |
1 | -3042 | 1521 | 2 | | | | | | | | | | |
| 0 | -1520 | 760 | 2 | | | | | | | | | |
| | 1 | -760 | 380 | 2 | | | | | | | | |
| | | 0 | -380 | 190 | 2 | | | | | | | |
| | | | 0 | -190 | 95 | 2 | | | | | | |
| | | | | 0 | -94 | 47 | 2 | | | | | |
| | | | | | 1 | -46 | 23 | 2 | | | | |
| | | | | | | 1 | -22 | 11 | 2 | | | |
| | | | | | | | 1 | -10 | 5 | 2 | | |
| | | | | | | | | 1 | -4 | 2 | 2 | |
| | | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 263671875*2 |
0 | .52734*2 |
1 | .05469*2 |
0 | .10938*2 |
0 | .21875*2 |
0 | .4375*2 |
0 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
6085.26367187510 = 1011111000101.0100001112
answer: 13705.2078 = 1011111000101.0100001112