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:
AB.616 = A B. 6 = A(=1010) B(=1011). 6(=0110) = 10101011.0112
answer: AB.616 = 10101011.0112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
10∙161+11∙160+6∙16-1 = 10∙16+11∙1+6∙0.0625 = 160+11+0.375 = 171.37510
got It: AB.616 =171.37510
Translate the number 171.37510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
171 | 2 | | | | | | | |
-170 | 85 | 2 | | | | | | |
1 | -84 | 42 | 2 | | | | | |
| 1 | -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. | 375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
171.37510 = 10101011.0112
answer: AB.616 = 10101011.0112