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:
B04.F16 = B 0 4. F = B(=1011) 0(=0000) 4(=0100). F(=1111) = 101100000100.11112
answer: B04.F16 = 101100000100.11112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
11∙162+0∙161+4∙160+15∙16-1 = 11∙256+0∙16+4∙1+15∙0.0625 = 2816+0+4+0.9375 = 2820.937510
got It: B04.F16 =2820.937510
Translate the number 2820.937510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
2820 | 2 | | | | | | | | | | | |
-2820 | 1410 | 2 | | | | | | | | | | |
0 | -1410 | 705 | 2 | | | | | | | | | |
| 0 | -704 | 352 | 2 | | | | | | | | |
| | 1 | -352 | 176 | 2 | | | | | | | |
| | | 0 | -176 | 88 | 2 | | | | | | |
| | | | 0 | -88 | 44 | 2 | | | | | |
| | | | | 0 | -44 | 22 | 2 | | | | |
| | | | | | 0 | -22 | 11 | 2 | | | |
| | | | | | | 0 | -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. | 9375*2 |
1 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
2820.937510 = 101100000100.11112
answer: B04.F16 = 101100000100.11112