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:
23578 = 2 3 5 7 = 2(=010) 3(=011) 5(=101) 7(=111) = 0100111011112
answer: 23578 = 100111011112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
2∙83+3∙82+5∙81+7∙80 = 2∙512+3∙64+5∙8+7∙1 = 1024+192+40+7 = 126310
got It: 23578 =126310
Translate the number 126310 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1263 | 2 | | | | | | | | | | |
-1262 | 631 | 2 | | | | | | | | | |
1 | -630 | 315 | 2 | | | | | | | | |
| 1 | -314 | 157 | 2 | | | | | | | |
| | 1 | -156 | 78 | 2 | | | | | | |
| | | 1 | -78 | 39 | 2 | | | | | |
| | | | 0 | -38 | 19 | 2 | | | | |
| | | | | 1 | -18 | 9 | 2 | | | |
| | | | | | 1 | -8 | 4 | 2 | | |
| | | | | | | 1 | -4 | 2 | 2 | |
| | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | 0 | | |
|
the result of the conversion was:
126310 = 100111011112
answer: 23578 = 100111011112