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:
BC.D616 = B C. D 6 = B(=1011) C(=1100). D(=1101) 6(=0110) = 10111100.11010112
answer: BC.D616 = 10111100.11010112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
11∙161+12∙160+13∙16-1+6∙16-2 = 11∙16+12∙1+13∙0.0625+6∙0.00390625 = 176+12+0.8125+0.0234375 = 188.835937510
got It: BC.D616 =188.835937510
Translate the number 188.835937510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
188 | 2 | | | | | | | |
-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. | 8359375*2 |
1 | .67188*2 |
1 | .34375*2 |
0 | .6875*2 |
1 | .375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
188.835937510 = 10111100.11010112
answer: BC.D616 = 10111100.11010112