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:
AAA.9916 = A A A. 9 9 = A(=1010) A(=1010) A(=1010). 9(=1001) 9(=1001) = 101010101010.100110012
answer: AAA.9916 = 101010101010.100110012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
10∙162+10∙161+10∙160+9∙16-1+9∙16-2 = 10∙256+10∙16+10∙1+9∙0.0625+9∙0.00390625 = 2560+160+10+0.5625+0.03515625 = 2730.5976562510
got It: AAA.9916 =2730.5976562510
Translate the number 2730.5976562510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
2730 | 2 | | | | | | | | | | | |
-2730 | 1365 | 2 | | | | | | | | | | |
0 | -1364 | 682 | 2 | | | | | | | | | |
| 1 | -682 | 341 | 2 | | | | | | | | |
| | 0 | -340 | 170 | 2 | | | | | | | |
| | | 1 | -170 | 85 | 2 | | | | | | |
| | | | 0 | -84 | 42 | 2 | | | | | |
| | | | | 1 | -42 | 21 | 2 | | | | |
| | | | | | 0 | -20 | 10 | 2 | | | |
| | | | | | | 1 | -10 | 5 | 2 | | |
| | | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 59765625*2 |
1 | .19531*2 |
0 | .39063*2 |
0 | .78125*2 |
1 | .5625*2 |
1 | .125*2 |
0 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
2730.5976562510 = 101010101010.100110012
answer: AAA.9916 = 101010101010.100110012