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:
507.632816 = 5 0 7. 6 3 2 8 = 5(=0101) 0(=0000) 7(=0111). 6(=0110) 3(=0011) 2(=0010) 8(=1000) = 10100000111.01100011001012
answer: 507.632816 = 10100000111.01100011001012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
5∙162+0∙161+7∙160+6∙16-1+3∙16-2+2∙16-3+8∙16-4 = 5∙256+0∙16+7∙1+6∙0.0625+3∙0.00390625+2∙0.000244140625+8∙1.52587890625E-5 = 1280+0+7+0.375+0.01171875+0.00048828125+0.0001220703125 = 1287.387329101562510
got It: 507.632816 =1287.387329101562510
Translate the number 1287.387329101562510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1287 | 2 | | | | | | | | | | |
-1286 | 643 | 2 | | | | | | | | | |
1 | -642 | 321 | 2 | | | | | | | | |
| 1 | -320 | 160 | 2 | | | | | | | |
| | 1 | -160 | 80 | 2 | | | | | | |
| | | 0 | -80 | 40 | 2 | | | | | |
| | | | 0 | -40 | 20 | 2 | | | | |
| | | | | 0 | -20 | 10 | 2 | | | |
| | | | | | 0 | -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. | 3873291015625*2 |
0 | .77466*2 |
1 | .54932*2 |
1 | .09863*2 |
0 | .19727*2 |
0 | .39453*2 |
0 | .78906*2 |
1 | .57813*2 |
1 | .15625*2 |
0 | .3125*2 |
0 | .625*2 |
the result of the conversion was:
1287.387329101562510 = 10100000111.01100011002
answer: 507.632816 = 10100000111.01100011002