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:
A96.28B16 = A 9 6. 2 8 B = A(=1010) 9(=1001) 6(=0110). 2(=0010) 8(=1000) B(=1011) = 101010010110.0010100010112
answer: A96.28B16 = 101010010110.0010100010112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
10∙162+9∙161+6∙160+2∙16-1+8∙16-2+11∙16-3 = 10∙256+9∙16+6∙1+2∙0.0625+8∙0.00390625+11∙0.000244140625 = 2560+144+6+0.125+0.03125+0.002685546875 = 2710.15893554687510
got It: A96.28B16 =2710.15893554687510
Translate the number 2710.15893554687510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
2710 | 2 | | | | | | | | | | | |
-2710 | 1355 | 2 | | | | | | | | | | |
0 | -1354 | 677 | 2 | | | | | | | | | |
| 1 | -676 | 338 | 2 | | | | | | | | |
| | 1 | -338 | 169 | 2 | | | | | | | |
| | | 0 | -168 | 84 | 2 | | | | | | |
| | | | 1 | -84 | 42 | 2 | | | | | |
| | | | | 0 | -42 | 21 | 2 | | | | |
| | | | | | 0 | -20 | 10 | 2 | | | |
| | | | | | | 1 | -10 | 5 | 2 | | |
| | | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 158935546875*2 |
0 | .31787*2 |
0 | .63574*2 |
1 | .27148*2 |
0 | .54297*2 |
1 | .08594*2 |
0 | .17188*2 |
0 | .34375*2 |
0 | .6875*2 |
1 | .375*2 |
0 | .75*2 |
the result of the conversion was:
2710.15893554687510 = 101010010110.00101000102
answer: A96.28B16 = 101010010110.00101000102