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:
55.02516 = 5 5. 0 2 5 = 5(=0101) 5(=0101). 0(=0000) 2(=0010) 5(=0101) = 1010101.0000001001012
answer: 55.02516 = 1010101.0000001001012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
5∙161+5∙160+0∙16-1+2∙16-2+5∙16-3 = 5∙16+5∙1+0∙0.0625+2∙0.00390625+5∙0.000244140625 = 80+5+0+0.0078125+0.001220703125 = 85.00903320312510
got It: 55.02516 =85.00903320312510
Translate the number 85.00903320312510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
85 | 2 | | | | | | |
-84 | 42 | 2 | | | | | |
1 | -42 | 21 | 2 | | | | |
| 0 | -20 | 10 | 2 | | | |
| | 1 | -10 | 5 | 2 | | |
| | | 0 | -4 | 2 | 2 | |
| | | | 1 | -2 | 1 | |
| | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 009033203125*2 |
0 | .01807*2 |
0 | .03613*2 |
0 | .07227*2 |
0 | .14453*2 |
0 | .28906*2 |
0 | .57813*2 |
1 | .15625*2 |
0 | .3125*2 |
0 | .625*2 |
1 | .25*2 |
the result of the conversion was:
85.00903320312510 = 1010101.00000010012
answer: 55.02516 = 1010101.00000010012