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:
Fa4516 = F a 4 5 = F(=1111) a(=1010) 4(=0100) 5(=0101) = 11111010010001012
answer: Fa4516 = 11111010010001012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙163+10∙162+4∙161+5∙160 = 15∙4096+10∙256+4∙16+5∙1 = 61440+2560+64+5 = 6406910
got It: Fa4516 =6406910
Translate the number 6406910 в binary like this:
the Integer part of the number is divided by the base of the new number system:
64069 | 2 | | | | | | | | | | | | | | | |
-64068 | 32034 | 2 | | | | | | | | | | | | | | |
1 | -32034 | 16017 | 2 | | | | | | | | | | | | | |
| 0 | -16016 | 8008 | 2 | | | | | | | | | | | | |
| | 1 | -8008 | 4004 | 2 | | | | | | | | | | | |
| | | 0 | -4004 | 2002 | 2 | | | | | | | | | | |
| | | | 0 | -2002 | 1001 | 2 | | | | | | | | | |
| | | | | 0 | -1000 | 500 | 2 | | | | | | | | |
| | | | | | 1 | -500 | 250 | 2 | | | | | | | |
| | | | | | | 0 | -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:
6406910 = 11111010010001012
answer: Fa4516 = 11111010010001012