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:
52.9816 = 5 2. 9 8 = 5(=0101) 2(=0010). 9(=1001) 8(=1000) = 1010010.100112
answer: 52.9816 = 1010010.100112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
5∙161+2∙160+9∙16-1+8∙16-2 = 5∙16+2∙1+9∙0.0625+8∙0.00390625 = 80+2+0.5625+0.03125 = 82.5937510
got It: 52.9816 =82.5937510
Translate the number 82.5937510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
82 | 2 | | | | | | |
-82 | 41 | 2 | | | | | |
0 | -40 | 20 | 2 | | | | |
| 1 | -20 | 10 | 2 | | | |
| | 0 | -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. | 59375*2 |
1 | .1875*2 |
0 | .375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
82.5937510 = 1010010.100112
answer: 52.9816 = 1010010.100112