What are the D flip-flop input expressions D1 and D0 for the 2-bit saturating counter in GATE CS 2026 Set-1 Q43?

D1 = P̄Q1 + P̄Q0 + Q1Q0 and D0 = P̄Q̄0 + P̄Q1 + Q1Q̄0. These are derived directly from the next state table using Karnaugh maps. For D flip-flops, D1=Q1+ and D0=Q0+. All eight rows of the truth table verify correctly against both expressions.

How does a 2-bit saturating counter work in GATE CS 2026 Set-1 Q43?

A 2-bit saturating counter counts up when P=0 and down when P=1, but saturates at the boundaries instead of wrapping around. When counting up and at state 11 (maximum), it stays at 11 instead of rolling over to 00. When counting down and at state 00 (minimum), it stays at 00 instead of rolling over to 11. This is the saturating behaviour reflected in the next state table.

How are D flip-flop inputs derived from the next state table in GATE CS 2026 Set-1 Q43?

For D flip-flops, the input equals the desired next state directly — D1=Q1+ and D0=Q0+. The next state values are read from the state table for each combination of P, Q1, Q0. A Karnaugh map is then applied to minimise D1 and D0 into sum-of-products expressions.

2-bit Saturating Up Down Counter D Flip-flop D1 D0 | GATE CS 2026 Set-1 Q43

Computer Sciences > GATE 2026 SET-1 > Sequential Circuits

Consider a 2-bit saturating up/down counter that performs the saturating up count when the input P is 0, and the saturating down count when P is 1. The Next State table of the counter is as shown below. 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, D₁ and D₀?

D₁ = PQ₁ + P̄Q₀ + Q₁Q̄₀ D₀ = PQ₀ + P̄Q₁ + Q₁Q̄₀

D₁ = P̄Q₁ + P̄Q₀ + Q₁Q₀ D₀ = P̄Q̄₀ + P̄Q₁ + Q₁Q̄₀

D₁ = P̄Q₁ + P̄Q₀ + Q₁Q₀ D₀ = P̄Q₀ + P̄Q₁ + Q₁Q̄₀

D₁ = PQ̄₁ + P̄Q₀ + Q₁Q₀ D₀ = PQ̄₀ + P̄Q₁ + Q₁Q̄₀

Correct : b

For D flip-flops, D1 = Q1⁺ and D0 = Q0⁺ directly from the next state table. Reading the next state values from the table and deriving the Boolean expressions using Karnaugh maps:
D1 = P̄Q1 + P̄Q0 + Q1Q0
P̄Q0 covers the cases where P=0 and Q0=1 (states 01 and 11 with P=0). P̄Q1 covers P=0 and Q1=1 (states 10 and 11 with P=0). Q1Q0 covers the single remaining case where P=1, Q1=1, Q0=1 (state 11 with P=1, which must go to 1). All eight rows verify correctly against the state table.
D0 = P̄Q̄0 + P̄Q1 + Q1Q̄0
P̄Q̄0 covers P=0 and Q0=0 (states 00 and 10 with P=0). P̄Q1 covers P=0 and Q1=1 (states 10 and 11 with P=0). Q1Q̄0 covers Q1=1 and Q0=0 (state 10 with P=1). All eight rows verify correctly against the state table.
Correct answer: B

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