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:
B89A.0316 = B 8 9 A. 0 3 = B(=1011) 8(=1000) 9(=1001) A(=1010). 0(=0000) 3(=0011) = 1011100010011010.000000112
answer: B89A.0316 = 1011100010011010.000000112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
11∙163+8∙162+9∙161+10∙160+0∙16-1+3∙16-2 = 11∙4096+8∙256+9∙16+10∙1+0∙0.0625+3∙0.00390625 = 45056+2048+144+10+0+0.01171875 = 47258.0117187510
got It: B89A.0316 =47258.0117187510
Translate the number 47258.0117187510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
47258 | 2 | | | | | | | | | | | | | | | |
-47258 | 23629 | 2 | | | | | | | | | | | | | | |
0 | -23628 | 11814 | 2 | | | | | | | | | | | | | |
| 1 | -11814 | 5907 | 2 | | | | | | | | | | | | |
| | 0 | -5906 | 2953 | 2 | | | | | | | | | | | |
| | | 1 | -2952 | 1476 | 2 | | | | | | | | | | |
| | | | 1 | -1476 | 738 | 2 | | | | | | | | | |
| | | | | 0 | -738 | 369 | 2 | | | | | | | | |
| | | | | | 0 | -368 | 184 | 2 | | | | | | | |
| | | | | | | 1 | -184 | 92 | 2 | | | | | | |
| | | | | | | | 0 | -92 | 46 | 2 | | | | | |
| | | | | | | | | 0 | -46 | 23 | 2 | | | | |
| | | | | | | | | | 0 | -22 | 11 | 2 | | | |
| | | | | | | | | | | 1 | -10 | 5 | 2 | | |
| | | | | | | | | | | | 1 | -4 | 2 | 2 | |
| | | | | | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 01171875*2 |
0 | .02344*2 |
0 | .04688*2 |
0 | .09375*2 |
0 | .1875*2 |
0 | .375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
47258.0117187510 = 1011100010011010.000000112
answer: B89A.0316 = 1011100010011010.000000112