GATE EE 2021 Set 1 — Question 47
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Analog & Digital Electronics → Digital Logic Circuits → Latches, Flip-Flops & Counters
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Question
A counter is constructed with three D flip-flops. The input-output pairs are named , , and , where the subscript 0 denotes the least significant bit. The output sequence is desired to be the Gray-code sequence 000, 001, 011, 010, 110, 111, 101, and 100, repeating periodically. Note that the bits are listed in the format. The combinational logic expression for is
Correct answer
(C) Q₂ Q₀ + Q₁ Q₀
Solution
To find the expression for , we first list the present state and next state based on the given Gray-code sequence:
For a D flip-flop, the input is equal to the next state . Thus, . Extracting from the table:
Grouping the 1s:
| Present State () | Next State () |
|---|---|
| 000 | 001 |
| 001 | 011 |
| 011 | 010 |
| 010 | 110 |
| 110 | 111 |
| 111 | 101 |
| 101 | 100 |
| 100 | 000 |
| 00 | 01 | 11 | 10 | |
|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 |
1.Group 1 (cells 001, 011):
2.Group 2 (cells 010, 110):
Therefore, .Continue learning with Success Tracker
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