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:
3CA.3B116 = 3 C A. 3 B 1 = 3(=0011) C(=1100) A(=1010). 3(=0011) B(=1011) 1(=0001) = 1111001010.0011101100012
answer: 3CA.3B116 = 1111001010.0011101100012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
3∙162+12∙161+10∙160+3∙16-1+11∙16-2+1∙16-3 = 3∙256+12∙16+10∙1+3∙0.0625+11∙0.00390625+1∙0.000244140625 = 768+192+10+0.1875+0.04296875+0.000244140625 = 970.23071289062510
got It: 3CA.3B116 =970.23071289062510
Translate the number 970.23071289062510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
970 | 2 | | | | | | | | | |
-970 | 485 | 2 | | | | | | | | |
0 | -484 | 242 | 2 | | | | | | | |
| 1 | -242 | 121 | 2 | | | | | | |
| | 0 | -120 | 60 | 2 | | | | | |
| | | 1 | -60 | 30 | 2 | | | | |
| | | | 0 | -30 | 15 | 2 | | | |
| | | | | 0 | -14 | 7 | 2 | | |
| | | | | | 1 | -6 | 3 | 2 | |
| | | | | | | 1 | -2 | 1 | |
| | | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 230712890625*2 |
0 | .46143*2 |
0 | .92285*2 |
1 | .8457*2 |
1 | .69141*2 |
1 | .38281*2 |
0 | .76563*2 |
1 | .53125*2 |
1 | .0625*2 |
0 | .125*2 |
0 | .25*2 |
the result of the conversion was:
970.23071289062510 = 1111001010.00111011002
answer: 3CA.3B116 = 1111001010.00111011002