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 hexadecimal to binary like this:
15101210.131416 = 1 5 1 0 1 2 1 0. 1 3 1 4 = 1(=0001) 5(=0101) 1(=0001) 0(=0000) 1(=0001) 2(=0010) 1(=0001) 0(=0000). 1(=0001) 3(=0011) 1(=0001) 4(=0100) = 10101000100000001001000010000.000100110001012
answer: 15101210.131416 = 10101000100000001001000010000.000100110001012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙167+5∙166+1∙165+0∙164+1∙163+2∙162+1∙161+0∙160+1∙16-1+3∙16-2+1∙16-3+4∙16-4 = 1∙268435456+5∙16777216+1∙1048576+0∙65536+1∙4096+2∙256+1∙16+0∙1+1∙0.0625+3∙0.00390625+1∙0.000244140625+4∙1.52587890625E-5 = 268435456+83886080+1048576+0+4096+512+16+0+0.0625+0.01171875+0.000244140625+6.103515625E-5 = 353374736.0745239257812510
got It: 15101210.131416 =353374736.0745239257812510
Translate the number 353374736.0745239257812510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
353374736 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
-353374736 | 176687368 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
0 | -176687368 | 88343684 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | |
| 0 | -88343684 | 44171842 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | |
| | 0 | -44171842 | 22085921 | 2 | | | | | | | | | | | | | | | | | | | | | | | | |
| | | 0 | -22085920 | 11042960 | 2 | | | | | | | | | | | | | | | | | | | | | | | |
| | | | 1 | -11042960 | 5521480 | 2 | | | | | | | | | | | | | | | | | | | | | | |
| | | | | 0 | -5521480 | 2760740 | 2 | | | | | | | | | | | | | | | | | | | | | |
| | | | | | 0 | -2760740 | 1380370 | 2 | | | | | | | | | | | | | | | | | | | | |
| | | | | | | 0 | -1380370 | 690185 | 2 | | | | | | | | | | | | | | | | | | | |
| | | | | | | | 0 | -690184 | 345092 | 2 | | | | | | | | | | | | | | | | | | |
| | | | | | | | | 1 | -345092 | 172546 | 2 | | | | | | | | | | | | | | | | | |
| | | | | | | | | | 0 | -172546 | 86273 | 2 | | | | | | | | | | | | | | | | |
| | | | | | | | | | | 0 | -86272 | 43136 | 2 | | | | | | | | | | | | | | | |
| | | | | | | | | | | | 1 | -43136 | 21568 | 2 | | | | | | | | | | | | | | |
| | | | | | | | | | | | | 0 | -21568 | 10784 | 2 | | | | | | | | | | | | | |
| | | | | | | | | | | | | | 0 | -10784 | 5392 | 2 | | | | | | | | | | | | |
| | | | | | | | | | | | | | | 0 | -5392 | 2696 | 2 | | | | | | | | | | | |
| | | | | | | | | | | | | | | | 0 | -2696 | 1348 | 2 | | | | | | | | | | |
| | | | | | | | | | | | | | | | | 0 | -1348 | 674 | 2 | | | | | | | | | |
| | | | | | | | | | | | | | | | | | 0 | -674 | 337 | 2 | | | | | | | | |
| | | | | | | | | | | | | | | | | | | 0 | -336 | 168 | 2 | | | | | | | |
| | | | | | | | | | | | | | | | | | | | 1 | -168 | 84 | 2 | | | | | | |
| | | | | | | | | | | | | | | | | | | | | 0 | -84 | 42 | 2 | | | | | |
| | | | | | | | | | | | | | | | | | | | | | 0 | -42 | 21 | 2 | | | | |
| | | | | | | | | | | | | | | | | | | | | | | 0 | -20 | 10 | 2 | | | |
| | | | | | | | | | | | | | | | | | | | | | | | 1 | -10 | 5 | 2 | | |
| | | | | | | | | | | | | | | | | | | | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 07452392578125*2 |
0 | .14905*2 |
0 | .2981*2 |
0 | .59619*2 |
1 | .19238*2 |
0 | .38477*2 |
0 | .76953*2 |
1 | .53906*2 |
1 | .07813*2 |
0 | .15625*2 |
0 | .3125*2 |
the result of the conversion was:
353374736.0745239257812510 = 10101000100000001001000010000.00010011002
answer: 15101210.131416 = 10101000100000001001000010000.00010011002