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:
F8DE7.416 = F 8 D E 7. 4 = F(=1111) 8(=1000) D(=1101) E(=1110) 7(=0111). 4(=0100) = 11111000110111100111.012
answer: F8DE7.416 = 11111000110111100111.012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙164+8∙163+13∙162+14∙161+7∙160+4∙16-1 = 15∙65536+8∙4096+13∙256+14∙16+7∙1+4∙0.0625 = 983040+32768+3328+224+7+0.25 = 1019367.2510
got It: F8DE7.416 =1019367.2510
Translate the number 1019367.2510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1019367 | 2 | | | | | | | | | | | | | | | | | | | |
-1019366 | 509683 | 2 | | | | | | | | | | | | | | | | | | |
1 | -509682 | 254841 | 2 | | | | | | | | | | | | | | | | | |
| 1 | -254840 | 127420 | 2 | | | | | | | | | | | | | | | | |
| | 1 | -127420 | 63710 | 2 | | | | | | | | | | | | | | | |
| | | 0 | -63710 | 31855 | 2 | | | | | | | | | | | | | | |
| | | | 0 | -31854 | 15927 | 2 | | | | | | | | | | | | | |
| | | | | 1 | -15926 | 7963 | 2 | | | | | | | | | | | | |
| | | | | | 1 | -7962 | 3981 | 2 | | | | | | | | | | | |
| | | | | | | 1 | -3980 | 1990 | 2 | | | | | | | | | | |
| | | | | | | | 1 | -1990 | 995 | 2 | | | | | | | | | |
| | | | | | | | | 0 | -994 | 497 | 2 | | | | | | | | |
| | | | | | | | | | 1 | -496 | 248 | 2 | | | | | | | |
| | | | | | | | | | | 1 | -248 | 124 | 2 | | | | | | |
| | | | | | | | | | | | 0 | -124 | 62 | 2 | | | | | |
| | | | | | | | | | | | | 0 | -62 | 31 | 2 | | | | |
| | | | | | | | | | | | | | 0 | -30 | 15 | 2 | | | |
| | | | | | | | | | | | | | | 1 | -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. | 25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
1019367.2510 = 11111000110111100111.012
answer: F8DE7.416 = 11111000110111100111.012