Question

Given below is the diagram of a synchronous sequential circuit with one J-K flip-flop and one T flip-flop with their outputs denoted as A and B respectively, with \( J_A = (A' + B') \), \( K_A = (A + B) \), and \( T_B = A \). Starting from the initial state \( AB = 00 \), the sequence of states \( (AB) \) visited by the circuit is 
 

• A. 00 \( \to \) 01 \( \to \) 10 \( \to \) 11 \( \to \) 00 \( \dots \)
• B. 00 \( \to \) 10 \( \to \) 01 \( \to \) 11 \( \to \) 00 \( \dots \)
• C. 00 \( \to \) 10 \( \to \) 11 \( \to \) 01 \( \to \) 00 \( \dots \)
• D. 00 \( \to \) 01 \( \to \) 11 \( \to \) 00 \( \dots \)

Hint:

In sequential circuits with flip-flops, analyze the J-K and T inputs based on the current state and the logic expressions for state transitions.

Answer 1

The Correct Option is B

We are given a sequential circuit with a J-K flip-flop and a T flip-flop. Let's analyze the state transitions. Step 1: Initial state \( AB = 00 \). We start from the initial state \( AB = 00 \). - The inputs for the J-K flip-flop are: \[ J_A = (A' + B') = (0 + 1) = 1, K_A = (A + B) = (0 + 0) = 0. \] This means the J-K flip-flop will set \( A = 1 \) and \( A' = 0 \). - The input for the T flip-flop is: \[ T_B = A = 0, \] so \( B \) will remain 0. Thus, the next state is \( AB = 10 \). Step 2: State \( AB = 10 \). - The inputs for the J-K flip-flop are: \[ J_A = (A' + B') = (1 + 0) = 1, K_A = (A + B) = (1 + 0) = 1. \] This means the J-K flip-flop will toggle \( A = 0 \). - The input for the T flip-flop is: \[ T_B = A = 1, \] so \( B \) will toggle to 1. Thus, the next state is \( AB = 01 \). Step 3: State \( AB = 01 \). - The inputs for the J-K flip-flop are: \[ J_A = (A' + B') = (1 + 1) = 1, K_A = (A + B) = (0 + 1) = 1. \] This means the J-K flip-flop will toggle \( A = 1 \). - The input for the T flip-flop is: \[ T_B = A = 1, \] so \( B \) will toggle to 0. Thus, the next state is \( AB = 11 \). Step 4: State \( AB = 11 \). - The inputs for the J-K flip-flop are: \[ J_A = (A' + B') = (0 + 0) = 0, K_A = (A + B) = (1 + 1) = 1. \] This means the J-K flip-flop will reset \( A = 0 \). - The input for the T flip-flop is: \[ T_B = A = 0, \] so \( B \) remains 0. Thus, the next state is \( AB = 00 \). Step 5: Conclusion. The sequence of states visited is \( 00 \to 10 \to 01 \to 11 \to 00 \dots \), which matches option (B). Final Answer: 00 \( \to \) 10 \( \to \) 01 \( \to \) 11 \( \to \) 00 \( \dots \)