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 $1010101000010111$.
