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:
610.A516 = 6 1 0. A 5 = 6(=0110) 1(=0001) 0(=0000). A(=1010) 5(=0101) = 11000010000.101001012
answer: 610.A516 = 11000010000.101001012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
6∙162+1∙161+0∙160+10∙16-1+5∙16-2 = 6∙256+1∙16+0∙1+10∙0.0625+5∙0.00390625 = 1536+16+0+0.625+0.01953125 = 1552.6445312510
got It: 610.A516 =1552.6445312510
Translate the number 1552.6445312510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1552 | 2 | | | | | | | | | | |
-1552 | 776 | 2 | | | | | | | | | |
0 | -776 | 388 | 2 | | | | | | | | |
| 0 | -388 | 194 | 2 | | | | | | | |
| | 0 | -194 | 97 | 2 | | | | | | |
| | | 0 | -96 | 48 | 2 | | | | | |
| | | | 1 | -48 | 24 | 2 | | | | |
| | | | | 0 | -24 | 12 | 2 | | | |
| | | | | | 0 | -12 | 6 | 2 | | |
| | | | | | | 0 | -6 | 3 | 2 | |
| | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 64453125*2 |
1 | .28906*2 |
0 | .57813*2 |
1 | .15625*2 |
0 | .3125*2 |
0 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
1552.6445312510 = 11000010000.101001012
answer: 610.A516 = 11000010000.101001012