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:
AF.B16 = A F. B = A(=1010) F(=1111). B(=1011) = 10101111.10112
answer: AF.B16 = 10101111.10112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
10∙161+15∙160+11∙16-1 = 10∙16+15∙1+11∙0.0625 = 160+15+0.6875 = 175.687510
got It: AF.B16 =175.687510
Translate the number 175.687510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
175 | 2 | | | | | | | |
-174 | 87 | 2 | | | | | | |
1 | -86 | 43 | 2 | | | | | |
| 1 | -42 | 21 | 2 | | | | |
| | 1 | -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. | 6875*2 |
1 | .375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
175.687510 = 10101111.10112
answer: AF.B16 = 10101111.10112