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:
FA716 = F A 7 = F(=1111) A(=1010) 7(=0111) = 1111101001112
answer: FA716 = 1111101001112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙162+10∙161+7∙160 = 15∙256+10∙16+7∙1 = 3840+160+7 = 400710
got It: FA716 =400710
Translate the number 400710 в binary like this:
the Integer part of the number is divided by the base of the new number system:
4007 | 2 | | | | | | | | | | | |
-4006 | 2003 | 2 | | | | | | | | | | |
1 | -2002 | 1001 | 2 | | | | | | | | | |
| 1 | -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:
400710 = 1111101001112
answer: FA716 = 1111101001112