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GATE CSE 2025 Session 1 Q60: Cycle length of a 4-flip-flop twisted ring counter

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 _________. (Answer in integer)

Four D flip-flops D0 to D3 on a common clock; Q0 feeds D1, Q1 feeds D2, Q2 feeds D3, and the complemented output of D3 (Q3 bar) is fed back to the input of D0
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Try it: numerical answer: type the value

Numerical answer. No negative marking.
Show answer and explanation

Answer: 7 to 8 (official GATE 2025 final answer key)

Concept used: A shift register with the inverted last output fed back is a Johnson (twisted ring) counter, which cycles through 2n2n states.

First step: Start from 0000 and clock it: the inverted Q3 shifts in, giving 1000, 1100, 1110, 1111, 0111, … until it returns to 0000.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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