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:
05ff16 = 0 5 f f = 0(=0000) 5(=0101) f(=1111) f(=1111) = 101111111112
answer: 05ff16 = 101111111112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
0∙163+5∙162+15∙161+15∙160 = 0∙4096+5∙256+15∙16+15∙1 = 0+1280+240+15 = 153510
got It: 05ff16 =153510
Translate the number 153510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1535 | 2 | | | | | | | | | | |
-1534 | 767 | 2 | | | | | | | | | |
1 | -766 | 383 | 2 | | | | | | | | |
| 1 | -382 | 191 | 2 | | | | | | | |
| | 1 | -190 | 95 | 2 | | | | | | |
| | | 1 | -94 | 47 | 2 | | | | | |
| | | | 1 | -46 | 23 | 2 | | | | |
| | | | | 1 | -22 | 11 | 2 | | | |
| | | | | | 1 | -10 | 5 | 2 | | |
| | | | | | | 1 | -4 | 2 | 2 | |
| | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | 0 | | |
|
the result of the conversion was:
153510 = 101111111112
answer: 05ff16 = 101111111112