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:
0b1111111116 = 0 b 1 1 1 1 1 1 1 1 = 0(=0000) b(=1011) 1(=0001) 1(=0001) 1(=0001) 1(=0001) 1(=0001) 1(=0001) 1(=0001) 1(=0001) = 1011000100010001000100010001000100012
answer: 0b1111111116 = 1011000100010001000100010001000100012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
0∙169+11∙168+1∙167+1∙166+1∙165+1∙164+1∙163+1∙162+1∙161+1∙160 = 0∙68719476736+11∙4294967296+1∙268435456+1∙16777216+1∙1048576+1∙65536+1∙4096+1∙256+1∙16+1∙1 = 0+47244640256+268435456+16777216+1048576+65536+4096+256+16+1 = 4753097140910
got It: 0b1111111116 =4753097140910
Translate the number 4753097140910 в binary like this:
the Integer part of the number is divided by the base of the new number system:
47530971409 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
-47530971408 | 23765485704 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
1 | -23765485704 | 11882742852 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| 0 | -11882742852 | 5941371426 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | 0 | -5941371426 | 2970685713 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | 0 | -2970685712 | 1485342856 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | 1 | -1485342856 | 742671428 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | 0 | -742671428 | 371335714 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | 0 | -371335714 | 185667857 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | 0 | -185667856 | 92833928 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | 1 | -92833928 | 46416964 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | 0 | -46416964 | 23208482 | 2 | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | 0 | -23208482 | 11604241 | 2 | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | 0 | -11604240 | 5802120 | 2 | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | 1 | -5802120 | 2901060 | 2 | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | 0 | -2901060 | 1450530 | 2 | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | 0 | -1450530 | 725265 | 2 | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | 0 | -725264 | 362632 | 2 | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | 1 | -362632 | 181316 | 2 | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | 0 | -181316 | 90658 | 2 | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | 0 | -90658 | 45329 | 2 | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | 0 | -45328 | 22664 | 2 | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | 1 | -22664 | 11332 | 2 | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | 0 | -11332 | 5666 | 2 | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | 0 | -5666 | 2833 | 2 | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | 0 | -2832 | 1416 | 2 | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | 1 | -1416 | 708 | 2 | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | 0 | -708 | 354 | 2 | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -354 | 177 | 2 | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -176 | 88 | 2 | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -88 | 44 | 2 | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -44 | 22 | 2 | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -22 | 11 | 2 | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -10 | 5 | 2 | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -4 | 2 | 2 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | | |
|
the result of the conversion was:
4753097140910 = 1011000100010001000100010001000100012
answer: 0b1111111116 = 1011000100010001000100010001000100012