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:
Fa516 = F a 5 = F(=1111) a(=1010) 5(=0101) = 1111101001012
answer: Fa516 = 1111101001012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙162+10∙161+5∙160 = 15∙256+10∙16+5∙1 = 3840+160+5 = 400510
got It: Fa516 =400510
Translate the number 400510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
4005 | 2 | | | | | | | | | | | |
-4004 | 2002 | 2 | | | | | | | | | | |
1 | -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:
400510 = 1111101001012
answer: Fa516 = 1111101001012