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:
101111.01118 = 1 0 1 1 1 1. 0 1 1 1 = 1(=001) 0(=000) 1(=001) 1(=001) 1(=001) 1(=001). 0(=000) 1(=001) 1(=001) 1(=001) = 001000001001001001.0000010010012
answer: 101111.01118 = 1000001001001001.0000010010012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙85+0∙84+1∙83+1∙82+1∙81+1∙80+0∙8-1+1∙8-2+1∙8-3+1∙8-4 = 1∙32768+0∙4096+1∙512+1∙64+1∙8+1∙1+0∙0.125+1∙0.015625+1∙0.001953125+1∙0.000244140625 = 32768+0+512+64+8+1+0+0.015625+0.001953125+0.000244140625 = 33353.01782226562510
got It: 101111.01118 =33353.01782226562510
Translate the number 33353.01782226562510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
33353 | 2 | | | | | | | | | | | | | | | |
-33352 | 16676 | 2 | | | | | | | | | | | | | | |
1 | -16676 | 8338 | 2 | | | | | | | | | | | | | |
| 0 | -8338 | 4169 | 2 | | | | | | | | | | | | |
| | 0 | -4168 | 2084 | 2 | | | | | | | | | | | |
| | | 1 | -2084 | 1042 | 2 | | | | | | | | | | |
| | | | 0 | -1042 | 521 | 2 | | | | | | | | | |
| | | | | 0 | -520 | 260 | 2 | | | | | | | | |
| | | | | | 1 | -260 | 130 | 2 | | | | | | | |
| | | | | | | 0 | -130 | 65 | 2 | | | | | | |
| | | | | | | | 0 | -64 | 32 | 2 | | | | | |
| | | | | | | | | 1 | -32 | 16 | 2 | | | | |
| | | | | | | | | | 0 | -16 | 8 | 2 | | | |
| | | | | | | | | | | 0 | -8 | 4 | 2 | | |
| | | | | | | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 017822265625*2 |
0 | .03564*2 |
0 | .07129*2 |
0 | .14258*2 |
0 | .28516*2 |
0 | .57031*2 |
1 | .14063*2 |
0 | .28125*2 |
0 | .5625*2 |
1 | .125*2 |
0 | .25*2 |
the result of the conversion was:
33353.01782226562510 = 1000001001001001.00000100102
answer: 101111.01118 = 1000001001001001.00000100102