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:
10.2116 = 1 0. 2 1 = 1(=0001) 0(=0000). 2(=0010) 1(=0001) = 10000.001000012
answer: 10.2116 = 10000.001000012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙161+0∙160+2∙16-1+1∙16-2 = 1∙16+0∙1+2∙0.0625+1∙0.00390625 = 16+0+0.125+0.00390625 = 16.1289062510
got It: 10.2116 =16.1289062510
Translate the number 16.1289062510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
16 | 2 | | | | |
-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. | 12890625*2 |
0 | .25781*2 |
0 | .51563*2 |
1 | .03125*2 |
0 | .0625*2 |
0 | .125*2 |
0 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
16.1289062510 = 10000.001000012
answer: 10.2116 = 10000.001000012