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:
1FFF16 = 1 F F F = 1(=0001) F(=1111) F(=1111) F(=1111) = 11111111111112
answer: 1FFF16 = 11111111111112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙163+15∙162+15∙161+15∙160 = 1∙4096+15∙256+15∙16+15∙1 = 4096+3840+240+15 = 819110
got It: 1FFF16 =819110
Translate the number 819110 в binary like this:
the Integer part of the number is divided by the base of the new number system:
8191 | 2 | | | | | | | | | | | | |
-8190 | 4095 | 2 | | | | | | | | | | | |
1 | -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:
819110 = 11111111111112
answer: 1FFF16 = 11111111111112