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:
FACD16 = F A C D = F(=1111) A(=1010) C(=1100) D(=1101) = 11111010110011012
answer: FACD16 = 11111010110011012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙163+10∙162+12∙161+13∙160 = 15∙4096+10∙256+12∙16+13∙1 = 61440+2560+192+13 = 6420510
got It: FACD16 =6420510
Translate the number 6420510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
64205 | 2 | | | | | | | | | | | | | | | |
-64204 | 32102 | 2 | | | | | | | | | | | | | | |
1 | -32102 | 16051 | 2 | | | | | | | | | | | | | |
| 0 | -16050 | 8025 | 2 | | | | | | | | | | | | |
| | 1 | -8024 | 4012 | 2 | | | | | | | | | | | |
| | | 1 | -4012 | 2006 | 2 | | | | | | | | | | |
| | | | 0 | -2006 | 1003 | 2 | | | | | | | | | |
| | | | | 0 | -1002 | 501 | 2 | | | | | | | | |
| | | | | | 1 | -500 | 250 | 2 | | | | | | | |
| | | | | | | 1 | -250 | 125 | 2 | | | | | | |
| | | | | | | | 0 | -124 | 62 | 2 | | | | | |
| | | | | | | | | 1 | -62 | 31 | 2 | | | | |
| | | | | | | | | | 0 | -30 | 15 | 2 | | | |
| | | | | | | | | | | 1 | -14 | 7 | 2 | | |
| | | | | | | | | | | | 1 | -6 | 3 | 2 | |
| | | | | | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | | | | | 1 | | |
|
the result of the conversion was:
6420510 = 11111010110011012
answer: FACD16 = 11111010110011012