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:
fdffffff16 = f d f f f f f f = f(=1111) d(=1101) f(=1111) f(=1111) f(=1111) f(=1111) f(=1111) f(=1111) = 111111011111111111111111111111112
answer: fdffffff16 = 111111011111111111111111111111112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙167+13∙166+15∙165+15∙164+15∙163+15∙162+15∙161+15∙160 = 15∙268435456+13∙16777216+15∙1048576+15∙65536+15∙4096+15∙256+15∙16+15∙1 = 4026531840+218103808+15728640+983040+61440+3840+240+15 = 426141286310
got It: fdffffff16 =426141286310
Translate the number 426141286310 в binary like this:
the Integer part of the number is divided by the base of the new number system:
4261412863 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
-4261412862 | 2130706431 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
1 | -2130706430 | 1065353215 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| 1 | -1065353214 | 532676607 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | 1 | -532676606 | 266338303 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | 1 | -266338302 | 133169151 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | 1 | -133169150 | 66584575 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | 1 | -66584574 | 33292287 | 2 | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | 1 | -33292286 | 16646143 | 2 | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | 1 | -16646142 | 8323071 | 2 | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | 1 | -8323070 | 4161535 | 2 | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | 1 | -4161534 | 2080767 | 2 | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | 1 | -2080766 | 1040383 | 2 | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | 1 | -1040382 | 520191 | 2 | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | 1 | -520190 | 260095 | 2 | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | 1 | -260094 | 130047 | 2 | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | 1 | -130046 | 65023 | 2 | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | 1 | -65022 | 32511 | 2 | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | 1 | -32510 | 16255 | 2 | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | 1 | -16254 | 8127 | 2 | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | 1 | -8126 | 4063 | 2 | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | 1 | -4062 | 2031 | 2 | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | 1 | -2030 | 1015 | 2 | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | 1 | -1014 | 507 | 2 | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | 1 | -506 | 253 | 2 | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | 1 | -252 | 126 | 2 | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | 1 | -126 | 63 | 2 | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | 0 | -62 | 31 | 2 | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -30 | 15 | 2 | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -14 | 7 | 2 | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -6 | 3 | 2 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | |
|
the result of the conversion was:
426141286310 = 111111011111111111111111111111112
answer: fdffffff16 = 111111011111111111111111111111112