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:
E7C.B16 = E 7 C. B = E(=1110) 7(=0111) C(=1100). B(=1011) = 111001111100.10112
answer: E7C.B16 = 111001111100.10112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
14∙162+7∙161+12∙160+11∙16-1 = 14∙256+7∙16+12∙1+11∙0.0625 = 3584+112+12+0.6875 = 3708.687510
got It: E7C.B16 =3708.687510
Translate the number 3708.687510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
3708 | 2 | | | | | | | | | | | |
-3708 | 1854 | 2 | | | | | | | | | | |
0 | -1854 | 927 | 2 | | | | | | | | | |
| 0 | -926 | 463 | 2 | | | | | | | | |
| | 1 | -462 | 231 | 2 | | | | | | | |
| | | 1 | -230 | 115 | 2 | | | | | | |
| | | | 1 | -114 | 57 | 2 | | | | | |
| | | | | 1 | -56 | 28 | 2 | | | | |
| | | | | | 1 | -28 | 14 | 2 | | | |
| | | | | | | 0 | -14 | 7 | 2 | | |
| | | | | | | | 0 | -6 | 3 | 2 | |
| | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 6875*2 |
1 | .375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
3708.687510 = 111001111100.10112
answer: E7C.B16 = 111001111100.10112