A synchronous counter is a type of sequential circuit that uses flip-flops to count and generate a sequence of binary numbers. In this case, we are designing a synchronous counter using JK flip-flops for the given sequence: 000, 101, 110, 111, 011, 010.



A JK flip-flop is a type of flip-flop that can be used to store one bit of information. It has two inputs: J (set) and K (reset), and two outputs: Q (output) and Q' (complement of output). The behavior of a JK flip-flop can be summarized as follows:

- When J=0 and K=0, the flip-flop holds its current state.
- When J=1 and K=0, the flip-flop sets to 1.
- When J=0 and K=1, the flip-flop resets to 0.
- When J=1 and K=1, the flip-flop toggles its state (Q' becomes the complement of Q).



To design a synchronous counter using JK flip-flops, we need to determine the number of flip-flops required based on the number of states in the sequence. In this case, the given sequence has 6 states (000, 101, 110, 111, 011, 010), so we will need 3 JK flip-flops.



Next, we need to create a state transition table that defines the inputs (J and K) for each flip-flop based on the desired sequence. The table will have 6 rows (corresponding to the 6 states) and 3 columns (corresponding to the 3 flip-flops).

```
State | J2 J1 J0
-----------------
000 | 0 0 0
101 | 1 0 1
110 | 1 1 0
111 | 1 1 1
011 | 0 1 1
010 | 0 1 0
```



Using the state transition table, we can now implement the circuit using JK flip-flops. Each flip-flop will have its J and K inputs connected to the corresponding column in the table.

- J2 and K2 inputs of the first flip-flop are connected to the J2 and K2 columns in the table.
- J1 and K1 inputs of the second flip-flop are connected to the J1 and K1 columns in the table.
- J0 and K0 inputs of the third flip-flop are connected to the J0 and K0 columns in the table.

The outputs (Q2, Q1, Q0) of the flip-flops represent the binary count. The circuit will have 3 outputs, each corresponding to the output of one flip-flop.



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