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 right
let\'s make a direct translation from binary to post-binary like this:
101111.0101010002 = 101 111. 010 101 000 = 101(=5) 111(=7). 010(=2) 101(=5) 000(=0) = 57.2508
answer: 101111.010101002 = 57.2508
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙25+0∙24+1∙23+1∙22+1∙21+1∙20+0∙2-1+1∙2-2+0∙2-3+1∙2-4+0∙2-5+1∙2-6+0∙2-7+0∙2-8+0∙2-9 = 1∙32+0∙16+1∙8+1∙4+1∙2+1∙1+0∙0.5+1∙0.25+0∙0.125+1∙0.0625+0∙0.03125+1∙0.015625+0∙0.0078125+0∙0.00390625+0∙0.001953125 = 32+0+8+4+2+1+0+0.25+0+0.0625+0+0.015625+0+0+0 = 47.32812510
got It: 101111.0101010002 =47.32812510
Translate the number 47.32812510 в octal like this:
the Integer part of the number is divided by the base of the new number system:
47 | 8 | |
-40 | 5 | |
7 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 328125*8 |
2 | .625*8 |
5 | .0*8 |
the result of the conversion was:
47.32812510 = 57.258
answer: 101111.010101002 = 57.258