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:
1F.D16 = 1 F. D = 1(=0001) F(=1111). D(=1101) = 11111.11012
answer: 1F.D16 = 11111.11012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙161+15∙160+13∙16-1 = 1∙16+15∙1+13∙0.0625 = 16+15+0.8125 = 31.812510
got It: 1F.D16 =31.812510
Translate the number 31.812510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
31 | 2 | | | | |
-30 | 15 | 2 | | | |
1 | -14 | 7 | 2 | | |
| 1 | -6 | 3 | 2 | |
| | 1 | -2 | 1 | |
| | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 8125*2 |
1 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
31.812510 = 11111.11012
answer: 1F.D16 = 11111.11012