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:
7041.3258 = 7 0 4 1. 3 2 5 = 7(=111) 0(=000) 4(=100) 1(=001). 3(=011) 2(=010) 5(=101) = 111000100001.0110101012
answer: 7041.3258 = 111000100001.0110101012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
7∙83+0∙82+4∙81+1∙80+3∙8-1+2∙8-2+5∙8-3 = 7∙512+0∙64+4∙8+1∙1+3∙0.125+2∙0.015625+5∙0.001953125 = 3584+0+32+1+0.375+0.03125+0.009765625 = 3617.41601562510
got It: 7041.3258 =3617.41601562510
Translate the number 3617.41601562510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
3617 | 2 | | | | | | | | | | | |
-3616 | 1808 | 2 | | | | | | | | | | |
1 | -1808 | 904 | 2 | | | | | | | | | |
| 0 | -904 | 452 | 2 | | | | | | | | |
| | 0 | -452 | 226 | 2 | | | | | | | |
| | | 0 | -226 | 113 | 2 | | | | | | |
| | | | 0 | -112 | 56 | 2 | | | | | |
| | | | | 1 | -56 | 28 | 2 | | | | |
| | | | | | 0 | -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. | 416015625*2 |
0 | .83203*2 |
1 | .66406*2 |
1 | .32813*2 |
0 | .65625*2 |
1 | .3125*2 |
0 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
3617.41601562510 = 111000100001.0110101012
answer: 7041.3258 = 111000100001.0110101012