GATE 2024 EC – Question 40
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 $AB$ 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 ______.
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Correct answer: (B) $\overline{D_3}D_2+\overline{D_3}\,\overline{D_1}$
Explanation
$B=1$ when the highest-priority active input is $D_2$ (code 01) or $D_0$ (code 11). $D_2$ is the highest active input when $D_3=0,D_2=1$: the term $\overline{D_3}D_2$. $D_0$ is the highest when $D_3=D_2=D_1=0$: the term $\overline{D_3}\,\overline{D_2}\,\overline{D_1}D_0$. Using the don't-care case where no input is active, the second term simplifies to $\overline{D_3}\,\overline{D_1}$ (with $D_2=0$ implied when it does not overlap with the first term). So $B=\overline{D_3}D_2+\overline{D_3}\,\overline{D_1}$.