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:
FFE.C16 = F F E. C = F(=1111) F(=1111) E(=1110). C(=1100) = 111111111110.112
the Final answer: FFE.C16 = 111111111110.112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙162+15∙161+14∙160+12∙16-1 = 15∙256+15∙16+14∙1+12∙0.0625 = 3840+240+14+0.75 = 4094.7510
got It: FFE.C16 =4094.7510
Translate the number 4094.7510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
4094 | 2 | | | | | | | | | | | |
-4094 | 2047 | 2 | | | | | | | | | | |
0 | -2046 | 1023 | 2 | | | | | | | | | |
| 1 | -1022 | 511 | 2 | | | | | | | | |
| | 1 | -510 | 255 | 2 | | | | | | | |
| | | 1 | -254 | 127 | 2 | | | | | | |
| | | | 1 | -126 | 63 | 2 | | | | | |
| | | | | 1 | -62 | 31 | 2 | | | | |
| | | | | | 1 | -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. | 75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
4094.7510 = 111111111110.112
the Final answer: FFE.C16 = 111111111110.112