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:
7F7FFFFF16 = 7 F 7 F F F F F = 7(=0111) F(=1111) 7(=0111) F(=1111) F(=1111) F(=1111) F(=1111) F(=1111) = 11111110111111111111111111111112
answer: 7F7FFFFF16 = 11111110111111111111111111111112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
7∙167+15∙166+7∙165+15∙164+15∙163+15∙162+15∙161+15∙160 = 7∙268435456+15∙16777216+7∙1048576+15∙65536+15∙4096+15∙256+15∙16+15∙1 = 1879048192+251658240+7340032+983040+61440+3840+240+15 = 213909503910
got It: 7F7FFFFF16 =213909503910
Translate the number 213909503910 в binary like this:
the Integer part of the number is divided by the base of the new number system:
2139095039 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
-2139095038 | 1069547519 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
1 | -1069547518 | 534773759 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| 1 | -534773758 | 267386879 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | 1 | -267386878 | 133693439 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | 1 | -133693438 | 66846719 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | 1 | -66846718 | 33423359 | 2 | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | 1 | -33423358 | 16711679 | 2 | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | 1 | -16711678 | 8355839 | 2 | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | 1 | -8355838 | 4177919 | 2 | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | 1 | -4177918 | 2088959 | 2 | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | 1 | -2088958 | 1044479 | 2 | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | 1 | -1044478 | 522239 | 2 | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | 1 | -522238 | 261119 | 2 | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | 1 | -261118 | 130559 | 2 | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | 1 | -130558 | 65279 | 2 | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | 1 | -65278 | 32639 | 2 | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | 1 | -32638 | 16319 | 2 | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | 1 | -16318 | 8159 | 2 | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | 1 | -8158 | 4079 | 2 | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | 1 | -4078 | 2039 | 2 | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | 1 | -2038 | 1019 | 2 | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | 1 | -1018 | 509 | 2 | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | 1 | -508 | 254 | 2 | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | 1 | -254 | 127 | 2 | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | 0 | -126 | 63 | 2 | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | 1 | -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:
213909503910 = 11111110111111111111111111111112
answer: 7F7FFFFF16 = 11111110111111111111111111111112