GATE EC 2024 Set 1 — Question 40
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Digital Circuits → Combinational Logic → Priority Encoders
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Question
A 4-bit priority encoder has inputs , and in descending order of priority. The two-bit output is generated as 00, 01, 10, and 11 corresponding to inputs , and , respectively. The Boolean expression of the output bit is _______.
Correct answer
(B) D₃ D₂ + D₃ D₁
Solution
The priority encoder has inputs with having the highest priority. The output is mapped as follows:
From the truth table, the expression for is:
Assuming the case where no input is active is a don't care or that is always 1 if others are 0, we can simplify the expression. Let's check the options.
For option (B):
| Input Condition | Output | Output |
|---|---|---|
| 0 | 0 | |
| 0 | 1 | |
| 1 | 0 | |
| 1 | 1 |
Assuming the case where no input is active is a don't care or that is always 1 if others are 0, we can simplify the expression. Let's check the options.
For option (B):
- If , . (Correct)
- If , . (Correct)
- If , . (Correct)
- If , . (Correct, covers )
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