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:
315.60216 = 3 1 5. 6 0 2 = 3(=0011) 1(=0001) 5(=0101). 6(=0110) 0(=0000) 2(=0010) = 1100010101.011000000012
answer: 315.60216 = 1100010101.011000000012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
3∙162+1∙161+5∙160+6∙16-1+0∙16-2+2∙16-3 = 3∙256+1∙16+5∙1+6∙0.0625+0∙0.00390625+2∙0.000244140625 = 768+16+5+0.375+0+0.00048828125 = 789.3754882812510
got It: 315.60216 =789.3754882812510
Translate the number 789.3754882812510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
789 | 2 | | | | | | | | | |
-788 | 394 | 2 | | | | | | | | |
1 | -394 | 197 | 2 | | | | | | | |
| 0 | -196 | 98 | 2 | | | | | | |
| | 1 | -98 | 49 | 2 | | | | | |
| | | 0 | -48 | 24 | 2 | | | | |
| | | | 1 | -24 | 12 | 2 | | | |
| | | | | 0 | -12 | 6 | 2 | | |
| | | | | | 0 | -6 | 3 | 2 | |
| | | | | | | 0 | -2 | 1 | |
| | | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 37548828125*2 |
0 | .75098*2 |
1 | .50195*2 |
1 | .00391*2 |
0 | .00781*2 |
0 | .01563*2 |
0 | .03125*2 |
0 | .0625*2 |
0 | .125*2 |
0 | .25*2 |
0 | .5*2 |
the result of the conversion was:
789.3754882812510 = 1100010101.01100000002
answer: 315.60216 = 1100010101.01100000002