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:
456.1128 = 4 5 6. 1 1 2 = 4(=100) 5(=101) 6(=110). 1(=001) 1(=001) 2(=010) = 100101110.0010010102
answer: 456.1128 = 100101110.001001012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
4∙82+5∙81+6∙80+1∙8-1+1∙8-2+2∙8-3 = 4∙64+5∙8+6∙1+1∙0.125+1∙0.015625+2∙0.001953125 = 256+40+6+0.125+0.015625+0.00390625 = 302.1445312510
got It: 456.1128 =302.1445312510
Translate the number 302.1445312510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
302 | 2 | | | | | | | | |
-302 | 151 | 2 | | | | | | | |
0 | -150 | 75 | 2 | | | | | | |
| 1 | -74 | 37 | 2 | | | | | |
| | 1 | -36 | 18 | 2 | | | | |
| | | 1 | -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. | 14453125*2 |
0 | .28906*2 |
0 | .57813*2 |
1 | .15625*2 |
0 | .3125*2 |
0 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
302.1445312510 = 100101110.001001012
answer: 456.1128 = 100101110.001001012