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:
3f5.5716 = 3 f 5. 5 7 = 3(=0011) f(=1111) 5(=0101). 5(=0101) 7(=0111) = 1111110101.010101112
answer: 3f5.5716 = 1111110101.010101112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
3∙162+15∙161+5∙160+5∙16-1+7∙16-2 = 3∙256+15∙16+5∙1+5∙0.0625+7∙0.00390625 = 768+240+5+0.3125+0.02734375 = 1013.3398437510
got It: 3f5.5716 =1013.3398437510
Translate the number 1013.3398437510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1013 | 2 | | | | | | | | | |
-1012 | 506 | 2 | | | | | | | | |
1 | -506 | 253 | 2 | | | | | | | |
| 0 | -252 | 126 | 2 | | | | | | |
| | 1 | -126 | 63 | 2 | | | | | |
| | | 0 | -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. | 33984375*2 |
0 | .67969*2 |
1 | .35938*2 |
0 | .71875*2 |
1 | .4375*2 |
0 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
1013.3398437510 = 1111110101.010101112
answer: 3f5.5716 = 1111110101.010101112