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:
FD216 = F D 2 = F(=1111) D(=1101) 2(=0010) = 1111110100102
answer: FD216 = 1111110100102
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙162+13∙161+2∙160 = 15∙256+13∙16+2∙1 = 3840+208+2 = 405010
got It: FD216 =405010
Translate the number 405010 в binary like this:
the Integer part of the number is divided by the base of the new number system:
4050 | 2 | | | | | | | | | | | |
-4050 | 2025 | 2 | | | | | | | | | | |
0 | -2024 | 1012 | 2 | | | | | | | | | |
| 1 | -1012 | 506 | 2 | | | | | | | | |
| | 0 | -506 | 253 | 2 | | | | | | | |
| | | 0 | -252 | 126 | 2 | | | | | | |
| | | | 1 | -126 | 63 | 2 | | | | | |
| | | | | 0 | -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:
405010 = 1111110100102
answer: FD216 = 1111110100102