GATE CS 2026 Set 1 — Question 37
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Digital Logic → Sequential Circuits → Counters (Sync, Async)
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Question
Consider a 2-bit saturating up/down counter that performs the saturating up count when the input is 0, and the saturating down count when is 1. The Next State table of the counter is as shown. The counter is built as a synchronous sequential circuit using D flip-flops.
Which one of the following options corresponds to the expressions for the inputs of the D flip-flops, and ?
| Input | Current State | Next State |
|---|---|---|
| 0 | 0 0 | 0 1 |
| 0 | 0 1 | 1 0 |
| 0 | 1 0 | 1 1 |
| 0 | 1 1 | 1 1 |
| 1 | 0 0 | 0 0 |
| 1 | 0 1 | 0 0 |
| 1 | 1 0 | 0 1 |
| 1 | 1 1 | 1 0 |
Correct answer
(B) D₁ = P Q₁ + P Q₀ + Q₁ Q₀ D₀ = P Q₀ + P Q₁ + Q₁ Q₀
Solution
To find the expressions for and , we treat the Next State bits and as the outputs of the combinational logic, with inputs . Since D flip-flops are used, and .For ():
From the table, is 1 for the following input combinations :
From the table, is 1 for the following input combinations :
From the table, is 1 for the following input combinations :
- Combine and :
- Combine and :
- Combine and :
From the table, is 1 for the following input combinations :
- Combine and :
- Combine and :
- Combine and :
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