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:
129.62516 = 1 2 9. 6 2 5 = 1(=0001) 2(=0010) 9(=1001). 6(=0110) 2(=0010) 5(=0101) = 100101001.0110001001012
answer: 129.62516 = 100101001.0110001001012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙162+2∙161+9∙160+6∙16-1+2∙16-2+5∙16-3 = 1∙256+2∙16+9∙1+6∙0.0625+2∙0.00390625+5∙0.000244140625 = 256+32+9+0.375+0.0078125+0.001220703125 = 297.38403320312510
got It: 129.62516 =297.38403320312510
Translate the number 297.38403320312510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
297 | 2 | | | | | | | | |
-296 | 148 | 2 | | | | | | | |
1 | -148 | 74 | 2 | | | | | | |
| 0 | -74 | 37 | 2 | | | | | |
| | 0 | -36 | 18 | 2 | | | | |
| | | 1 | -18 | 9 | 2 | | | |
| | | | 0 | -8 | 4 | 2 | | |
| | | | | 1 | -4 | 2 | 2 | |
| | | | | | 0 | -2 | 1 | |
| | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 384033203125*2 |
0 | .76807*2 |
1 | .53613*2 |
1 | .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:
297.38403320312510 = 100101001.01100010012
answer: 129.62516 = 100101001.01100010012