The correct answer is $\boxed{\text{D8F9}_{16}}$.
To convert a binary number to hexadecimal, we divide the binary number into groups of four bits, starting from the right. Each group of four bits is then converted to a hexadecimal digit using the following table:
| Binary | Hexadecimal |
|—|—|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | A |
| 1011 | B |
| 1100 | C |
| 1101 | D |
| 1110 | E |
| 1111 | F |
For example, the binary number $1010101000010111$ can be divided into the following groups of four bits:
$10101010$
$00010111$
The first group of four bits, $10101010$, is converted to the hexadecimal digit $\text{D}$. The second group of four bits, $00010111$, is converted to the hexadecimal digit $\text{F}$. Therefore, the hexadecimal equivalent of the binary number $1010101000010111$ is $\text{D8F9}_{16}$.
The other options are incorrect because they do not represent the correct hexadecimal equivalent of the binary number $1010101000010111$.