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:
47.5716 = 4 7. 5 7 = 4(=0100) 7(=0111). 5(=0101) 7(=0111) = 1000111.010101112
answer: 47.5716 = 1000111.010101112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
4∙161+7∙160+5∙16-1+7∙16-2 = 4∙16+7∙1+5∙0.0625+7∙0.00390625 = 64+7+0.3125+0.02734375 = 71.3398437510
got It: 47.5716 =71.3398437510
Translate the number 71.3398437510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
71 | 2 | | | | | | |
-70 | 35 | 2 | | | | | |
1 | -34 | 17 | 2 | | | | |
| 1 | -16 | 8 | 2 | | | |
| | 1 | -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. | 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:
71.3398437510 = 1000111.010101112
answer: 47.5716 = 1000111.010101112