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:
1A.B116 = 1 A. B 1 = 1(=0001) A(=1010). B(=1011) 1(=0001) = 11010.101100012
answer: 1A.B116 = 11010.101100012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙161+10∙160+11∙16-1+1∙16-2 = 1∙16+10∙1+11∙0.0625+1∙0.00390625 = 16+10+0.6875+0.00390625 = 26.6914062510
got It: 1A.B116 =26.6914062510
Translate the number 26.6914062510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
26 | 2 | | | | |
-26 | 13 | 2 | | | |
0 | -12 | 6 | 2 | | |
| 1 | -6 | 3 | 2 | |
| | 0 | -2 | 1 | |
| | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 69140625*2 |
1 | .38281*2 |
0 | .76563*2 |
1 | .53125*2 |
1 | .0625*2 |
0 | .125*2 |
0 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
26.6914062510 = 11010.101100012
answer: 1A.B116 = 11010.101100012