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:
15.1216 = 1 5. 1 2 = 1(=0001) 5(=0101). 1(=0001) 2(=0010) = 10101.00010012
answer: 15.1216 = 10101.00010012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙161+5∙160+1∙16-1+2∙16-2 = 1∙16+5∙1+1∙0.0625+2∙0.00390625 = 16+5+0.0625+0.0078125 = 21.070312510
got It: 15.1216 =21.070312510
Translate the number 21.070312510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
21 | 2 | | | | |
-20 | 10 | 2 | | | |
1 | -10 | 5 | 2 | | |
| 0 | -4 | 2 | 2 | |
| | 1 | -2 | 1 | |
| | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 0703125*2 |
0 | .14063*2 |
0 | .28125*2 |
0 | .5625*2 |
1 | .125*2 |
0 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
21.070312510 = 10101.00010012
answer: 15.1216 = 10101.00010012