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:
BCDE.A16 = B C D E. A = B(=1011) C(=1100) D(=1101) E(=1110). A(=1010) = 1011110011011110.1012
the Final answer: BCDE.A16 = 1011110011011110.1012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
11∙163+12∙162+13∙161+14∙160+10∙16-1 = 11∙4096+12∙256+13∙16+14∙1+10∙0.0625 = 45056+3072+208+14+0.625 = 48350.62510
got It: BCDE.A16 =48350.62510
Translate the number 48350.62510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
48350 | 2 | | | | | | | | | | | | | | | |
-48350 | 24175 | 2 | | | | | | | | | | | | | | |
0 | -24174 | 12087 | 2 | | | | | | | | | | | | | |
| 1 | -12086 | 6043 | 2 | | | | | | | | | | | | |
| | 1 | -6042 | 3021 | 2 | | | | | | | | | | | |
| | | 1 | -3020 | 1510 | 2 | | | | | | | | | | |
| | | | 1 | -1510 | 755 | 2 | | | | | | | | | |
| | | | | 0 | -754 | 377 | 2 | | | | | | | | |
| | | | | | 1 | -376 | 188 | 2 | | | | | | | |
| | | | | | | 1 | -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. | 625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
48350.62510 = 1011110011011110.1012
the Final answer: BCDE.A16 = 1011110011011110.1012