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:
31C.DE16 = 3 1 C. D E = 3(=0011) 1(=0001) C(=1100). D(=1101) E(=1110) = 1100011100.11011112
answer: 31C.DE16 = 1100011100.11011112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
3∙162+1∙161+12∙160+13∙16-1+14∙16-2 = 3∙256+1∙16+12∙1+13∙0.0625+14∙0.00390625 = 768+16+12+0.8125+0.0546875 = 796.867187510
got It: 31C.DE16 =796.867187510
Translate the number 796.867187510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
796 | 2 | | | | | | | | | |
-796 | 398 | 2 | | | | | | | | |
0 | -398 | 199 | 2 | | | | | | | |
| 0 | -198 | 99 | 2 | | | | | | |
| | 1 | -98 | 49 | 2 | | | | | |
| | | 1 | -48 | 24 | 2 | | | | |
| | | | 1 | -24 | 12 | 2 | | | |
| | | | | 0 | -12 | 6 | 2 | | |
| | | | | | 0 | -6 | 3 | 2 | |
| | | | | | | 0 | -2 | 1 | |
| | | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 8671875*2 |
1 | .73438*2 |
1 | .46875*2 |
0 | .9375*2 |
1 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
796.867187510 = 1100011100.11011112
answer: 31C.DE16 = 1100011100.11011112