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:
BC1.3016 = B C 1. 3 0 = B(=1011) C(=1100) 1(=0001). 3(=0011) 0(=0000) = 101111000001.00112
answer: BC1.3016 = 101111000001.00112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
11∙162+12∙161+1∙160+3∙16-1+0∙16-2 = 11∙256+12∙16+1∙1+3∙0.0625+0∙0.00390625 = 2816+192+1+0.1875+0 = 3009.187510
got It: BC1.3016 =3009.187510
Translate the number 3009.187510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
3009 | 2 | | | | | | | | | | | |
-3008 | 1504 | 2 | | | | | | | | | | |
1 | -1504 | 752 | 2 | | | | | | | | | |
| 0 | -752 | 376 | 2 | | | | | | | | |
| | 0 | -376 | 188 | 2 | | | | | | | |
| | | 0 | -188 | 94 | 2 | | | | | | |
| | | | 0 | -94 | 47 | 2 | | | | | |
| | | | | 0 | -46 | 23 | 2 | | | | |
| | | | | | 1 | -22 | 11 | 2 | | | |
| | | | | | | 1 | -10 | 5 | 2 | | |
| | | | | | | | 1 | -4 | 2 | 2 | |
| | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 1875*2 |
0 | .375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
3009.187510 = 101111000001.00112
answer: BC1.3016 = 101111000001.00112