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:
37.4616 = 3 7. 4 6 = 3(=0011) 7(=0111). 4(=0100) 6(=0110) = 110111.01000112
answer: 37.4616 = 110111.01000112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
3∙161+7∙160+4∙16-1+6∙16-2 = 3∙16+7∙1+4∙0.0625+6∙0.00390625 = 48+7+0.25+0.0234375 = 55.273437510
got It: 37.4616 =55.273437510
Translate the number 55.273437510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
55 | 2 | | | | | |
-54 | 27 | 2 | | | | |
1 | -26 | 13 | 2 | | | |
| 1 | -12 | 6 | 2 | | |
| | 1 | -6 | 3 | 2 | |
| | | 0 | -2 | 1 | |
| | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 2734375*2 |
0 | .54688*2 |
1 | .09375*2 |
0 | .1875*2 |
0 | .375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
55.273437510 = 110111.01000112
answer: 37.4616 = 110111.01000112