Project ForgeConsider a sequential circuit with two positive edge-triggered D flip-flops in series (in→D1, Q1→D2, Q2→out), sharing the same clock. The number of states in the state transition diagram of this circuit that have a transition back to the SAME state on some value of 'in' is ____.
Explanation
State = (Q1,Q2); next state = (in, Q1), since D1=in and D2=Q1. State 00: with in=0, next=(0,0)=00 — self-loop. State 01: neither in=0 (→00) nor in=1 (→10) equals 01 — no self-loop. State 10: neither in=0 (→01) nor in=1 (→11) equals 10 — no self-loop. State 11: with in=1, next=(1,1)=11 — self-loop. So exactly 2 states (00 and 11) have a self-loop.
Source: GATE CS 2018 (2018)
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