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:
543.4128 = 5 4 3. 4 1 2 = 5(=101) 4(=100) 3(=011). 4(=100) 1(=001) 2(=010) = 101100011.1000010102
answer: 543.4128 = 101100011.100001012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
5∙82+4∙81+3∙80+4∙8-1+1∙8-2+2∙8-3 = 5∙64+4∙8+3∙1+4∙0.125+1∙0.015625+2∙0.001953125 = 320+32+3+0.5+0.015625+0.00390625 = 355.5195312510
got It: 543.4128 =355.5195312510
Translate the number 355.5195312510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
355 | 2 | | | | | | | | |
-354 | 177 | 2 | | | | | | | |
1 | -176 | 88 | 2 | | | | | | |
| 1 | -88 | 44 | 2 | | | | | |
| | 0 | -44 | 22 | 2 | | | | |
| | | 0 | -22 | 11 | 2 | | | |
| | | | 0 | -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. | 51953125*2 |
1 | .03906*2 |
0 | .07813*2 |
0 | .15625*2 |
0 | .3125*2 |
0 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
355.5195312510 = 101100011.100001012
answer: 543.4128 = 101100011.100001012