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:
0fff16 = 0 f f f = 0(=0000) f(=1111) f(=1111) f(=1111) = 1111111111112
answer: 0fff16 = 1111111111112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
0∙163+15∙162+15∙161+15∙160 = 0∙4096+15∙256+15∙16+15∙1 = 0+3840+240+15 = 409510
got It: 0fff16 =409510
Translate the number 409510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
4095 | 2 | | | | | | | | | | | |
-4094 | 2047 | 2 | | | | | | | | | | |
1 | -2046 | 1023 | 2 | | | | | | | | | |
| 1 | -1022 | 511 | 2 | | | | | | | | |
| | 1 | -510 | 255 | 2 | | | | | | | |
| | | 1 | -254 | 127 | 2 | | | | | | |
| | | | 1 | -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:
409510 = 1111111111112
answer: 0fff16 = 1111111111112