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:
ABF216 = A B F 2 = A(=1010) B(=1011) F(=1111) 2(=0010) = 10101011111100102
answer: ABF216 = 10101011111100102
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
10∙163+11∙162+15∙161+2∙160 = 10∙4096+11∙256+15∙16+2∙1 = 40960+2816+240+2 = 4401810
got It: ABF216 =4401810
Translate the number 4401810 в binary like this:
the Integer part of the number is divided by the base of the new number system:
44018 | 2 | | | | | | | | | | | | | | | |
-44018 | 22009 | 2 | | | | | | | | | | | | | | |
0 | -22008 | 11004 | 2 | | | | | | | | | | | | | |
| 1 | -11004 | 5502 | 2 | | | | | | | | | | | | |
| | 0 | -5502 | 2751 | 2 | | | | | | | | | | | |
| | | 0 | -2750 | 1375 | 2 | | | | | | | | | | |
| | | | 1 | -1374 | 687 | 2 | | | | | | | | | |
| | | | | 1 | -686 | 343 | 2 | | | | | | | | |
| | | | | | 1 | -342 | 171 | 2 | | | | | | | |
| | | | | | | 1 | -170 | 85 | 2 | | | | | | |
| | | | | | | | 1 | -84 | 42 | 2 | | | | | |
| | | | | | | | | 1 | -42 | 21 | 2 | | | | |
| | | | | | | | | | 0 | -20 | 10 | 2 | | | |
| | | | | | | | | | | 1 | -10 | 5 | 2 | | |
| | | | | | | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | | | | | 0 | | |
|
the result of the conversion was:
4401810 = 10101011111100102
answer: ABF216 = 10101011111100102