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:
/> | 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 $1010101000010111$.