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:
1f95.3a16 = 1 f 9 5. 3 a = 1(=0001) f(=1111) 9(=1001) 5(=0101). 3(=0011) a(=1010) = 1111110010101.00111012
answer: 1f95.3a16 = 1111110010101.00111012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙163+15∙162+9∙161+5∙160+3∙16-1+10∙16-2 = 1∙4096+15∙256+9∙16+5∙1+3∙0.0625+10∙0.00390625 = 4096+3840+144+5+0.1875+0.0390625 = 8085.226562510
got It: 1f95.3a16 =8085.226562510
Translate the number 8085.226562510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
8085 | 2 | | | | | | | | | | | | |
-8084 | 4042 | 2 | | | | | | | | | | | |
1 | -4042 | 2021 | 2 | | | | | | | | | | |
| 0 | -2020 | 1010 | 2 | | | | | | | | | |
| | 1 | -1010 | 505 | 2 | | | | | | | | |
| | | 0 | -504 | 252 | 2 | | | | | | | |
| | | | 1 | -252 | 126 | 2 | | | | | | |
| | | | | 0 | -126 | 63 | 2 | | | | | |
| | | | | | 0 | -62 | 31 | 2 | | | | |
| | | | | | | 1 | -30 | 15 | 2 | | | |
| | | | | | | | 1 | -14 | 7 | 2 | | |
| | | | | | | | | 1 | -6 | 3 | 2 | |
| | | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 2265625*2 |
0 | .45313*2 |
0 | .90625*2 |
1 | .8125*2 |
1 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
8085.226562510 = 1111110010101.00111012
answer: 1f95.3a16 = 1111110010101.00111012