This transfer is possible in two ways: direct transfer and using the decimal system.
first, let\'s make a direct transfer.
Fill in the number with missing zeros on the left
Fill in the number with missing zeros on the right
let\'s make a direct translation from binary to post-binary like this:
011001110101.1011102 = 011 001 110 101. 101 110 = 011(=3) 001(=1) 110(=6) 101(=5). 101(=5) 110(=6) = 3165.568
answer: 11001110101.101112 = 3165.568
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
0∙211+1∙210+1∙29+0∙28+0∙27+1∙26+1∙25+1∙24+0∙23+1∙22+0∙21+1∙20+1∙2-1+0∙2-2+1∙2-3+1∙2-4+1∙2-5+0∙2-6 = 0∙2048+1∙1024+1∙512+0∙256+0∙128+1∙64+1∙32+1∙16+0∙8+1∙4+0∙2+1∙1+1∙0.5+0∙0.25+1∙0.125+1∙0.0625+1∙0.03125+0∙0.015625 = 0+1024+512+0+0+64+32+16+0+4+0+1+0.5+0+0.125+0.0625+0.03125+0 = 1653.7187510
got It: 011001110101.1011102 =1653.7187510
Translate the number 1653.7187510 в octal like this:
the Integer part of the number is divided by the base of the new number system:
1653 | 8 | | | |
-1648 | 206 | 8 | | |
5 | -200 | 25 | 8 | |
| 6 | -24 | 3 | |
| | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 71875*8 |
5 | .75*8 |
6 | .0*8 |
the result of the conversion was:
1653.7187510 = 3165.568
answer: 11001110101.101112 = 3165.568