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:
AB12.CF16 = A B 1 2. C F = A(=1010) B(=1011) 1(=0001) 2(=0010). C(=1100) F(=1111) = 1010101100010010.110011112
answer: AB12.CF16 = 1010101100010010.110011112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
10∙163+11∙162+1∙161+2∙160+12∙16-1+15∙16-2 = 10∙4096+11∙256+1∙16+2∙1+12∙0.0625+15∙0.00390625 = 40960+2816+16+2+0.75+0.05859375 = 43794.8085937510
got It: AB12.CF16 =43794.8085937510
Translate the number 43794.8085937510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
43794 | 2 | | | | | | | | | | | | | | | |
-43794 | 21897 | 2 | | | | | | | | | | | | | | |
0 | -21896 | 10948 | 2 | | | | | | | | | | | | | |
| 1 | -10948 | 5474 | 2 | | | | | | | | | | | | |
| | 0 | -5474 | 2737 | 2 | | | | | | | | | | | |
| | | 0 | -2736 | 1368 | 2 | | | | | | | | | | |
| | | | 1 | -1368 | 684 | 2 | | | | | | | | | |
| | | | | 0 | -684 | 342 | 2 | | | | | | | | |
| | | | | | 0 | -342 | 171 | 2 | | | | | | | |
| | | | | | | 0 | -170 | 85 | 2 | | | | | | |
| | | | | | | | 1 | -84 | 42 | 2 | | | | | |
| | | | | | | | | 1 | -42 | 21 | 2 | | | | |
| | | | | | | | | | 0 | -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. | 80859375*2 |
1 | .61719*2 |
1 | .23438*2 |
0 | .46875*2 |
0 | .9375*2 |
1 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
43794.8085937510 = 1010101100010010.110011112
answer: AB12.CF16 = 1010101100010010.110011112