Consider a 2-bit saturating up/down counter. The saturating up count occurs when input P=0, and satu

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Question

Consider a 2-bit saturating up/down counter. The saturating up count occurs when input P=0, and saturating down count when P=1. Given the Next State table, which option gives the correct expressions for D flip-flop inputs D1 and D0?

Accepted Answer

Correct Answer: (B)Concept -- Sequential Circuit Design with K‑Map (Saturating Counter): A 2‑bit saturating counter has states 00,01,10,11. When P=0 (up), it increments unless already at 11 (saturates at 11). When P=1 (down), it decrements unless already at 00 (saturates at 00). The next state (Q1+, Q0+) is a function of current state (Q1,Q0) and input P. For D flip‑flops, D1 = Q1+, D0 = Q0+. Construct truth table (8 rows) and minimize using K‑maps. The correct minimized expressions are: D1 = P'Q1 + P'Q0 + Q1Q0, D0 = P'Q0' + P'Q1 + Q1Q0'. Option B matches this (note P'Q0' is equivalent to P' * (not Q0)). The other options either have wrong terms or wrong polarities. Saturating counters are common in digital systems (e.g., branch prediction) and the design procedure is standard.

Consider a 2-bit saturating up/down counter. The saturating up count occurs when input P=0, and saturating down count when P=1. Given the Next State table, which option gives the correct expressions for D flip-flop inputs D1 and D0?

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Consider a 2-bit saturating up/down counter. The saturating up count occurs when input P=0, and saturating down count when P=1. Given the Next State table, which option gives the correct expressions for D flip-flop inputs D1 and D0?

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