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:
1010.10116 = 1 0 1 0. 1 0 1 = 1(=0001) 0(=0000) 1(=0001) 0(=0000). 1(=0001) 0(=0000) 1(=0001) = 1000000010000.0001000000012
answer: 1010.10116 = 1000000010000.0001000000012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙163+0∙162+1∙161+0∙160+1∙16-1+0∙16-2+1∙16-3 = 1∙4096+0∙256+1∙16+0∙1+1∙0.0625+0∙0.00390625+1∙0.000244140625 = 4096+0+16+0+0.0625+0+0.000244140625 = 4112.06274414062510
got It: 1010.10116 =4112.06274414062510
Translate the number 4112.06274414062510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
4112 | 2 | | | | | | | | | | | | |
-4112 | 2056 | 2 | | | | | | | | | | | |
0 | -2056 | 1028 | 2 | | | | | | | | | | |
| 0 | -1028 | 514 | 2 | | | | | | | | | |
| | 0 | -514 | 257 | 2 | | | | | | | | |
| | | 0 | -256 | 128 | 2 | | | | | | | |
| | | | 1 | -128 | 64 | 2 | | | | | | |
| | | | | 0 | -64 | 32 | 2 | | | | | |
| | | | | | 0 | -32 | 16 | 2 | | | | |
| | | | | | | 0 | -16 | 8 | 2 | | | |
| | | | | | | | 0 | -8 | 4 | 2 | | |
| | | | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 062744140625*2 |
0 | .12549*2 |
0 | .25098*2 |
0 | .50195*2 |
1 | .00391*2 |
0 | .00781*2 |
0 | .01563*2 |
0 | .03125*2 |
0 | .0625*2 |
0 | .125*2 |
0 | .25*2 |
the result of the conversion was:
4112.06274414062510 = 1000000010000.00010000002
answer: 1010.10116 = 1000000010000.00010000002