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:
DB56.CD416 = D B 5 6. C D 4 = D(=1101) B(=1011) 5(=0101) 6(=0110). C(=1100) D(=1101) 4(=0100) = 1101101101010110.11001101012
answer: DB56.CD416 = 1101101101010110.11001101012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
13∙163+11∙162+5∙161+6∙160+12∙16-1+13∙16-2+4∙16-3 = 13∙4096+11∙256+5∙16+6∙1+12∙0.0625+13∙0.00390625+4∙0.000244140625 = 53248+2816+80+6+0.75+0.05078125+0.0009765625 = 56150.801757812510
got It: DB56.CD416 =56150.801757812510
Translate the number 56150.801757812510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
56150 | 2 | | | | | | | | | | | | | | | |
-56150 | 28075 | 2 | | | | | | | | | | | | | | |
0 | -28074 | 14037 | 2 | | | | | | | | | | | | | |
| 1 | -14036 | 7018 | 2 | | | | | | | | | | | | |
| | 1 | -7018 | 3509 | 2 | | | | | | | | | | | |
| | | 0 | -3508 | 1754 | 2 | | | | | | | | | | |
| | | | 1 | -1754 | 877 | 2 | | | | | | | | | |
| | | | | 0 | -876 | 438 | 2 | | | | | | | | |
| | | | | | 1 | -438 | 219 | 2 | | | | | | | |
| | | | | | | 0 | -218 | 109 | 2 | | | | | | |
| | | | | | | | 1 | -108 | 54 | 2 | | | | | |
| | | | | | | | | 1 | -54 | 27 | 2 | | | | |
| | | | | | | | | | 0 | -26 | 13 | 2 | | | |
| | | | | | | | | | | 1 | -12 | 6 | 2 | | |
| | | | | | | | | | | | 1 | -6 | 3 | 2 | |
| | | | | | | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 8017578125*2 |
1 | .60352*2 |
1 | .20703*2 |
0 | .41406*2 |
0 | .82813*2 |
1 | .65625*2 |
1 | .3125*2 |
0 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
56150.801757812510 = 1101101101010110.11001101012
answer: DB56.CD416 = 1101101101010110.11001101012