Question

A JK flip-flop with J=K=1 behaves as:

• A. Reset
• B. Set
• C. Toggle
• D. Hold

Hint:

The toggle behavior under \( J = K = 1 \) is the primary reason why the JK flip-flop is used to design T flip-flops and binary counters.
Always remember that \( Q_{n+1} = Q'_n \) in this state.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the behavior of a JK flip-flop when both control inputs \( J \) and \( K \) are held at logic high (\( 1 \)).
The JK flip-flop is a modification of the SR flip-flop to eliminate the invalid/unpredictable state when both inputs are high.

Step 2: Key Formula or Approach:
The operation of the JK flip-flop is governed by its characteristic equation:
\[ Q_{n+1} = J Q'_n + K' Q_n \] Where:
\( Q_n \) is the present state of the output.
\( Q_{n+1} \) is the next state of the output.
By substituting the values of \( J \) and \( K \) into the characteristic equation, we can determine the exact logic behavior.

Step 3: Detailed Explanation:
Let us analyze the truth table and behavior of the JK flip-flop for all input combinations:

• Case 1: \( J = 0, K = 0 \) (Hold mode):
\[ Q_{n+1} = 0 \cdot Q'_n + 1 \cdot Q_n = Q_n \] The output remains unchanged.

• Case 2: \( J = 0, K = 1 \) (Reset mode):
\[ Q_{n+1} = 0 \cdot Q'_n + 0 \cdot Q_n = 0 \] The output is cleared to zero.

• Case 3: \( J = 1, K = 0 \) (Set mode):
\[ Q_{n+1} = 1 \cdot Q'_n + 1 \cdot Q_n = Q'_n + Q_n = 1 \] The output is set to one.

• Case 4: \( J = 1, K = 1 \) (Toggle mode):
\[ Q_{n+1} = 1 \cdot Q'_n + 0 \cdot Q_n = Q'_n \] The output becomes the complement of its previous state. This is known as the toggle state.

Step 4: Final Answer:
Therefore, a JK flip-flop with \( J = K = 1 \) behaves as a Toggle flip-flop.