A $4$-bit priority encoder has inputs $D_{3}, D_{2}, D_{1}$, and $D_{0}$ in descending order of priority. The two-bit output $A B$ is generated as $00,01,10$, and 11 corresponding to inputs $D_{3}, D_{2}, D_{1}$, and $D_{0}$, respectively. The Boolean expression of the output bit $B$ is $\_\_\_\_\_\_\_$.
- $\overline{D_{3}} \overline{D_{2}}$
- $\overline{D_{3}} D_{2}+\overline{D_{3}} \overline{D_{1}}$
- $D_{3} \overline{D_{2}}+\overline{D_{3}} D_{1}$
- $\overline{D_{3}} \overline{D_{1}}$