Designing a synchronous up-down counter with JK flip-flop that counts the odd numbers from 1 to 7 in binary involves the following steps:

1. **Identify the number of Flip-Flops needed**: Since we are counting from 1 to 7, we need 3 flip-flops (2^3 = 8, which covers our range of 0-7).

2. **State Table Creation**: Create a state table for the counter. Since we are only interested in odd numbers from 1 to 7, the states will be 001, 011, 101, 111 (representing 1, 3, 5, 7 in binary respectively).

3. **Flip-Flop Transition Table**: Create a transition table for the JK flip-flop. This table will help us to know the required inputs (J and K) to transition from the current state to the next state.

4. **Karnaugh Maps and Boolean Expressions**: Use Karnaugh maps to simplify the Boolean expressions for each J and K input of the flip-flops.

5. **Circuit Design**: Draw the circuit diagram for the counter using the JK flip-flops and the Boolean expressions obtained from the Karnaugh maps. The circuit should include the flip-flops, AND gates, OR gates and NOT gates as required.

6. **Test the Counter**: Finally, verify the operation of the counter by simulating it or implementing it on a breadboard or FPGA. The counter should count up and down through the odd numbers from 1 to 7 in binary.

Please note that the exact design will depend on the specific JK flip-flop used and the desired counting sequence.

Question

Designing a synchronous up-down counter with JK flip-flop that counts the odd numbers from 1 to 7 in binary involves the following steps:

1. **Identify the number of Flip-Flops needed**: Since we are counting from 1 to 7, we need 3 flip-flops (2^3 = 8, which covers our range of 0-7).

2. **State Table Creation**: Create a state table for the counter. Since we are only interested in odd numbers from 1 to 7, the states will be 001, 011, 101, 111 (representing 1, 3, 5, 7 in binary respectively).

3. **Flip-Flop Transition Table**: Create a transition table for the JK flip-flop. This table will help us to know the required inputs (J and K) to transition from the current state to the next state.

4. **Karnaugh Maps and Boolean Expressions**: Use Karnaugh maps to simplify the Boolean expressions for each J and K input of the flip-flops.

5. **Circuit Design**: Draw the circuit diagram for the counter using the JK flip-flops and the Boolean expressions obtained from the Karnaugh maps. The circuit should include the flip-flops, AND gates, OR gates and NOT gates as required.

6. **Test the Counter**: Finally, verify the operation of the counter by simulating it or implementing it on a breadboard or FPGA. The counter should count up and down through the odd numbers from 1 to 7 in binary.

Please note that the exact design will depend on the specific JK flip-flop used and the desired counting sequence.

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