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:
1527.3628 = 1 5 2 7. 3 6 2 = 1(=001) 5(=101) 2(=010) 7(=111). 3(=011) 6(=110) 2(=010) = 001101010111.0111100102
answer: 1527.3628 = 1101010111.011110012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙83+5∙82+2∙81+7∙80+3∙8-1+6∙8-2+2∙8-3 = 1∙512+5∙64+2∙8+7∙1+3∙0.125+6∙0.015625+2∙0.001953125 = 512+320+16+7+0.375+0.09375+0.00390625 = 855.4726562510
got It: 1527.3628 =855.4726562510
Translate the number 855.4726562510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
855 | 2 | | | | | | | | | |
-854 | 427 | 2 | | | | | | | | |
1 | -426 | 213 | 2 | | | | | | | |
| 1 | -212 | 106 | 2 | | | | | | |
| | 1 | -106 | 53 | 2 | | | | | |
| | | 0 | -52 | 26 | 2 | | | | |
| | | | 1 | -26 | 13 | 2 | | | |
| | | | | 0 | -12 | 6 | 2 | | |
| | | | | | 1 | -6 | 3 | 2 | |
| | | | | | | 0 | -2 | 1 | |
| | | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 47265625*2 |
0 | .94531*2 |
1 | .89063*2 |
1 | .78125*2 |
1 | .5625*2 |
1 | .125*2 |
0 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
855.4726562510 = 1101010111.011110012
answer: 1527.3628 = 1101010111.011110012