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:
172.128 = 1 7 2. 1 2 = 1(=001) 7(=111) 2(=010). 1(=001) 2(=010) = 001111010.0010102
answer: 172.128 = 1111010.001012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙82+7∙81+2∙80+1∙8-1+2∙8-2 = 1∙64+7∙8+2∙1+1∙0.125+2∙0.015625 = 64+56+2+0.125+0.03125 = 122.1562510
got It: 172.128 =122.1562510
Translate the number 122.1562510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
122 | 2 | | | | | | |
-122 | 61 | 2 | | | | | |
0 | -60 | 30 | 2 | | | | |
| 1 | -30 | 15 | 2 | | | |
| | 0 | -14 | 7 | 2 | | |
| | | 1 | -6 | 3 | 2 | |
| | | | 1 | -2 | 1 | |
| | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 15625*2 |
0 | .3125*2 |
0 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
122.1562510 = 1111010.001012
answer: 172.128 = 1111010.001012