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:
00110101.11018 = 0 0 1 1 0 1 0 1. 1 1 0 1 = 0(=000) 0(=000) 1(=001) 1(=001) 0(=000) 1(=001) 0(=000) 1(=001). 1(=001) 1(=001) 0(=000) 1(=001) = 000000001001000001000001.0010010000012
answer: 00110101.11018 = 1001000001000001.0010010000012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
0∙87+0∙86+1∙85+1∙84+0∙83+1∙82+0∙81+1∙80+1∙8-1+1∙8-2+0∙8-3+1∙8-4 = 0∙2097152+0∙262144+1∙32768+1∙4096+0∙512+1∙64+0∙8+1∙1+1∙0.125+1∙0.015625+0∙0.001953125+1∙0.000244140625 = 0+0+32768+4096+0+64+0+1+0.125+0.015625+0+0.000244140625 = 36929.14086914062510
got It: 00110101.11018 =36929.14086914062510
Translate the number 36929.14086914062510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
36929 | 2 | | | | | | | | | | | | | | | |
-36928 | 18464 | 2 | | | | | | | | | | | | | | |
1 | -18464 | 9232 | 2 | | | | | | | | | | | | | |
| 0 | -9232 | 4616 | 2 | | | | | | | | | | | | |
| | 0 | -4616 | 2308 | 2 | | | | | | | | | | | |
| | | 0 | -2308 | 1154 | 2 | | | | | | | | | | |
| | | | 0 | -1154 | 577 | 2 | | | | | | | | | |
| | | | | 0 | -576 | 288 | 2 | | | | | | | | |
| | | | | | 1 | -288 | 144 | 2 | | | | | | | |
| | | | | | | 0 | -144 | 72 | 2 | | | | | | |
| | | | | | | | 0 | -72 | 36 | 2 | | | | | |
| | | | | | | | | 0 | -36 | 18 | 2 | | | | |
| | | | | | | | | | 0 | -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. | 140869140625*2 |
0 | .28174*2 |
0 | .56348*2 |
1 | .12695*2 |
0 | .25391*2 |
0 | .50781*2 |
1 | .01563*2 |
0 | .03125*2 |
0 | .0625*2 |
0 | .125*2 |
0 | .25*2 |
the result of the conversion was:
36929.14086914062510 = 1001000001000001.00100100002
answer: 00110101.11018 = 1001000001000001.00100100002