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:
FABC16 = F A B C = F(=1111) A(=1010) B(=1011) C(=1100) = 11111010101111002
answer: FABC16 = 11111010101111002
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙163+10∙162+11∙161+12∙160 = 15∙4096+10∙256+11∙16+12∙1 = 61440+2560+176+12 = 6418810
got It: FABC16 =6418810
Translate the number 6418810 в binary like this:
the Integer part of the number is divided by the base of the new number system:
64188 | 2 | | | | | | | | | | | | | | | |
-64188 | 32094 | 2 | | | | | | | | | | | | | | |
0 | -32094 | 16047 | 2 | | | | | | | | | | | | | |
| 0 | -16046 | 8023 | 2 | | | | | | | | | | | | |
| | 1 | -8022 | 4011 | 2 | | | | | | | | | | | |
| | | 1 | -4010 | 2005 | 2 | | | | | | | | | | |
| | | | 1 | -2004 | 1002 | 2 | | | | | | | | | |
| | | | | 1 | -1002 | 501 | 2 | | | | | | | | |
| | | | | | 0 | -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:
6418810 = 11111010101111002
answer: FABC16 = 11111010101111002