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:
F5A.7E16 = F 5 A. 7 E = F(=1111) 5(=0101) A(=1010). 7(=0111) E(=1110) = 111101011010.01111112
answer: F5A.7E16 = 111101011010.01111112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙162+5∙161+10∙160+7∙16-1+14∙16-2 = 15∙256+5∙16+10∙1+7∙0.0625+14∙0.00390625 = 3840+80+10+0.4375+0.0546875 = 3930.492187510
got It: F5A.7E16 =3930.492187510
Translate the number 3930.492187510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
3930 | 2 | | | | | | | | | | | |
-3930 | 1965 | 2 | | | | | | | | | | |
0 | -1964 | 982 | 2 | | | | | | | | | |
| 1 | -982 | 491 | 2 | | | | | | | | |
| | 0 | -490 | 245 | 2 | | | | | | | |
| | | 1 | -244 | 122 | 2 | | | | | | |
| | | | 1 | -122 | 61 | 2 | | | | | |
| | | | | 0 | -60 | 30 | 2 | | | | |
| | | | | | 1 | -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. | 4921875*2 |
0 | .98438*2 |
1 | .96875*2 |
1 | .9375*2 |
1 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
3930.492187510 = 111101011010.01111112
answer: F5A.7E16 = 111101011010.01111112