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:
F03.A316 = F 0 3. A 3 = F(=1111) 0(=0000) 3(=0011). A(=1010) 3(=0011) = 111100000011.101000112
answer: F03.A316 = 111100000011.101000112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙162+0∙161+3∙160+10∙16-1+3∙16-2 = 15∙256+0∙16+3∙1+10∙0.0625+3∙0.00390625 = 3840+0+3+0.625+0.01171875 = 3843.6367187510
got It: F03.A316 =3843.6367187510
Translate the number 3843.6367187510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
3843 | 2 | | | | | | | | | | | |
-3842 | 1921 | 2 | | | | | | | | | | |
1 | -1920 | 960 | 2 | | | | | | | | | |
| 1 | -960 | 480 | 2 | | | | | | | | |
| | 0 | -480 | 240 | 2 | | | | | | | |
| | | 0 | -240 | 120 | 2 | | | | | | |
| | | | 0 | -120 | 60 | 2 | | | | | |
| | | | | 0 | -60 | 30 | 2 | | | | |
| | | | | | 0 | -30 | 15 | 2 | | | |
| | | | | | | 0 | -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. | 63671875*2 |
1 | .27344*2 |
0 | .54688*2 |
1 | .09375*2 |
0 | .1875*2 |
0 | .375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
3843.6367187510 = 111100000011.101000112
answer: F03.A316 = 111100000011.101000112