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:
F2b16 = F 2 b = F(=1111) 2(=0010) b(=1011) = 1111001010112
answer: F2b16 = 1111001010112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙162+2∙161+11∙160 = 15∙256+2∙16+11∙1 = 3840+32+11 = 388310
got It: F2b16 =388310
Translate the number 388310 в binary like this:
the Integer part of the number is divided by the base of the new number system:
3883 | 2 | | | | | | | | | | | |
-3882 | 1941 | 2 | | | | | | | | | | |
1 | -1940 | 970 | 2 | | | | | | | | | |
| 1 | -970 | 485 | 2 | | | | | | | | |
| | 0 | -484 | 242 | 2 | | | | | | | |
| | | 1 | -242 | 121 | 2 | | | | | | |
| | | | 0 | -120 | 60 | 2 | | | | | |
| | | | | 1 | -60 | 30 | 2 | | | | |
| | | | | | 0 | -30 | 15 | 2 | | | |
| | | | | | | 0 | -14 | 7 | 2 | | |
| | | | | | | | 1 | -6 | 3 | 2 | |
| | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | 1 | | |
|
the result of the conversion was:
388310 = 1111001010112
answer: F2b16 = 1111001010112