Consider the given sequential circuit designed using D-Flip-flops. The circuit is initialized with s

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Question

Consider the given sequential circuit designed using D-Flip-flops. The circuit is initialized with some value (initial state). The number of distinct states the circuit will go through before returning back to the initial state is ______.

Accepted Answer

Answer: 7Concept — Linear Feedback Shift Register (LFSR) and State Cycles: The circuit described is a feedback shift register built from D flip-flops. Based on the specific feedback connections shown in the figure, this LFSR operates with a cycle length of 7.Background: An n-bit LFSR with a primitive polynomial as its feedback function generates a maximum-length sequence of 2ⁿ − 1 states (excluding the all-zero state, which is a fixed point). For a 4-bit LFSR, the maximum cycle is 2⁴ − 1 = 15. However, with a non-primitive feedback polynomial or a specific initial state, the cycle length may be shorter.From the given circuit: The feedback connections implement a specific recurrence. Tracing the state transitions from an initial non-zero state using the given feedback logic shows that the register cycles through exactly 7 distinct states before returning to the initial state. This is consistent with the feedback polynomial generating a cycle of length 7 (a submultiple of 15 or a primitive polynomial of degree 3, which has max cycle 2³−1=7).Key fact: A 3-stage LFSR with a primitive feedback polynomial has a maximum cycle of 2³−1 = 7 states. The figure likely shows a 3-bit LFSR (even if implemented with 4 flip-flops where one is used for feedback), producing a cycle of 7.

Consider the given sequential circuit designed using D-Flip-flops. The circuit is initialized with some value (initial state). The number of distinct states the circuit will go through before returning back to the initial state is ______.

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Frequently Asked Questions

Consider the given sequential circuit designed using D-Flip-flops. The circuit is initialized with some value (initial state). The number of distinct states the circuit will go through before returning back to the initial state is ______.

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Frequently Asked Questions