Project ForgeDigital Logic
Combinational & Sequential Circuits
GATE 2016
Expert
We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of J-K flip-flops required to implement this counter is ____.
3.5(± 0.5 accepted)
Explanation
The output '0' appears 3 times with 3 DIFFERENT next-states (→1, →2, →3), so a state machine based purely on output value would be non-deterministic unless each occurrence of '0' is its own distinct internal state. Total distinct states needed: 3 (for the three 0's) + 1 + 1 + 1 (for 1,2,3) = 6 states, needing ⌈log₂6⌉ = 3 flip-flops minimum (the source's own key accepts 3 or 4).
Source: GATE CS 2016 (Session 1 / Set A) (2016)
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