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:
010101011.1100110102 = 010 101 011. 110 011 010 = 010(=2) 101(=5) 011(=3). 110(=6) 011(=3) 010(=2) = 253.6328
answer: 10101011.110011012 = 253.6328
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
0∙28+1∙27+0∙26+1∙25+0∙24+1∙23+0∙22+1∙21+1∙20+1∙2-1+1∙2-2+0∙2-3+0∙2-4+1∙2-5+1∙2-6+0∙2-7+1∙2-8+0∙2-9 = 0∙256+1∙128+0∙64+1∙32+0∙16+1∙8+0∙4+1∙2+1∙1+1∙0.5+1∙0.25+0∙0.125+0∙0.0625+1∙0.03125+1∙0.015625+0∙0.0078125+1∙0.00390625+0∙0.001953125 = 0+128+0+32+0+8+0+2+1+0.5+0.25+0+0+0.03125+0.015625+0+0.00390625+0 = 171.8007812510
got It: 010101011.1100110102 =171.8007812510
Translate the number 171.8007812510 в octal like this:
the Integer part of the number is divided by the base of the new number system:
171 | 8 | | |
-168 | 21 | 8 | |
3 | -16 | 2 | |
| 5 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 80078125*8 |
6 | .40625*8 |
3 | .25*8 |
2 | .0*8 |
the result of the conversion was:
171.8007812510 = 253.6328
answer: 10101011.110011012 = 253.6328