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:
BEF.FDA16 = B E F. F D A = B(=1011) E(=1110) F(=1111). F(=1111) D(=1101) A(=1010) = 101111101111.111111011012
answer: BEF.FDA16 = 101111101111.111111011012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
11∙162+14∙161+15∙160+15∙16-1+13∙16-2+10∙16-3 = 11∙256+14∙16+15∙1+15∙0.0625+13∙0.00390625+10∙0.000244140625 = 2816+224+15+0.9375+0.05078125+0.00244140625 = 3055.9907226562510
got It: BEF.FDA16 =3055.9907226562510
Translate the number 3055.9907226562510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
3055 | 2 | | | | | | | | | | | |
-3054 | 1527 | 2 | | | | | | | | | | |
1 | -1526 | 763 | 2 | | | | | | | | | |
| 1 | -762 | 381 | 2 | | | | | | | | |
| | 1 | -380 | 190 | 2 | | | | | | | |
| | | 1 | -190 | 95 | 2 | | | | | | |
| | | | 0 | -94 | 47 | 2 | | | | | |
| | | | | 1 | -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. | 99072265625*2 |
1 | .98145*2 |
1 | .96289*2 |
1 | .92578*2 |
1 | .85156*2 |
1 | .70313*2 |
1 | .40625*2 |
0 | .8125*2 |
1 | .625*2 |
1 | .25*2 |
0 | .5*2 |
the result of the conversion was:
3055.9907226562510 = 101111101111.11111101102
answer: BEF.FDA16 = 101111101111.11111101102