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:
110.01016 = 1 1 0. 0 1 0 = 1(=0001) 1(=0001) 0(=0000). 0(=0000) 1(=0001) 0(=0000) = 100010000.000000012
answer: 110.01016 = 100010000.000000012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙162+1∙161+0∙160+0∙16-1+1∙16-2+0∙16-3 = 1∙256+1∙16+0∙1+0∙0.0625+1∙0.00390625+0∙0.000244140625 = 256+16+0+0+0.00390625+0 = 272.0039062510
got It: 110.01016 =272.0039062510
Translate the number 272.0039062510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
272 | 2 | | | | | | | | |
-272 | 136 | 2 | | | | | | | |
0 | -136 | 68 | 2 | | | | | | |
| 0 | -68 | 34 | 2 | | | | | |
| | 0 | -34 | 17 | 2 | | | | |
| | | 0 | -16 | 8 | 2 | | | |
| | | | 1 | -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. | 00390625*2 |
0 | .00781*2 |
0 | .01563*2 |
0 | .03125*2 |
0 | .0625*2 |
0 | .125*2 |
0 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
272.0039062510 = 100010000.000000012
answer: 110.01016 = 100010000.000000012