Topic: Digital Circuits
The state transition diagram for the diagram given is
- A. Q=0, Q=1 with S transitions (Next state = S)
- B. various graphs
- C. various graphs
- D. various graphs
Answer: A. Q=0, Q=1 with S transitions (Next state = S)
Explanation: From the circuit, the 2:1 Multiplexer selects between the T flip-flop's true output $Q$ (at $i_0$) and its complemented output $\bar{Q}$ (at $i_1$) based on the select line $S$. Therefore, the T input is $T = \bar{S}Q + S\bar{Q} = S \oplus Q$. The characteristic equation of a T flip-flop is $Q_{next} = T \oplus Q$. Substituting our T expression, we get $Q_{next} = (S \oplus Q) \oplus Q = S \oplus (Q \oplus Q) = S \oplus 0 = S$. This means the next state completely follows input $S$, which perfectly matches the state transition diagram shown in option (a).