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:
101.FE16 = 1 0 1. F E = 1(=0001) 0(=0000) 1(=0001). F(=1111) E(=1110) = 100000001.11111112
answer: 101.FE16 = 100000001.11111112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙162+0∙161+1∙160+15∙16-1+14∙16-2 = 1∙256+0∙16+1∙1+15∙0.0625+14∙0.00390625 = 256+0+1+0.9375+0.0546875 = 257.992187510
got It: 101.FE16 =257.992187510
Translate the number 257.992187510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
257 | 2 | | | | | | | | |
-256 | 128 | 2 | | | | | | | |
1 | -128 | 64 | 2 | | | | | | |
| 0 | -64 | 32 | 2 | | | | | |
| | 0 | -32 | 16 | 2 | | | | |
| | | 0 | -16 | 8 | 2 | | | |
| | | | 0 | -8 | 4 | 2 | | |
| | | | | 0 | -4 | 2 | 2 | |
| | | | | | 0 | -2 | 1 | |
| | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 9921875*2 |
1 | .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:
257.992187510 = 100000001.11111112
answer: 101.FE16 = 100000001.11111112