Question

The Race-around occurs when:

• A. Clock width small
• B. Clock width $>$ propagation delay
• C. Input zero
• D. Output constant

Hint:

To entirely eliminate the race-around condition, switch from level-triggering to edge-triggering or use a Master-Slave JK flip-flop.
The relation is simply: \( \text{Clock pulse width } (t_p) > \text{Propagation delay } (t_{pd}) \).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks under what physical conditions the "Race-around" phenomenon occurs in digital sequential circuits, specifically within level-triggered JK flip-flops.
Race-around is an undesirable condition that causes the output to oscillate uncontrollably.

Step 2: Key Formula or Approach:
For a level-triggered JK flip-flop in the toggle mode (\( J = K = 1 \)), the output is expected to complement once per clock pulse.
However, if the clock pulse duration (\( T_w \)) is significantly longer than the propagation delay of the logic gates inside the flip-flop (\( \Delta t \)), the output will toggle multiple times during a single active clock level.
Mathematically, the condition for race-around to occur is:
\[ T_w > \Delta t \]

Step 3: Detailed Explanation:
Let us explore the dynamics of this condition in detail:

• Level-Triggered Activation: During a level-triggered clock pulse, the inputs are active as long as the clock signal is high.

• Feedback Paths: In a JK flip-flop, the outputs \( Q \) and \( Q' \) are cross-coupled as feedback to the input gates.

• Continuous Toggling: When \( J = K = 1 \), the output immediately starts to change.
Once the output changes (after a small propagation delay \( \Delta t \)), the new state is fed back to the inputs.
If the clock is still high (because \( T_w > \Delta t \)), the flip-flop will toggle again, and this cycle repeats continuously as long as the clock remains high.

• Unpredictable State: At the falling edge of the clock pulse, the final state of the output is completely unpredictable and depends on whether the clock width was an exact multiple of the delay.

• Methods of prevention: This issue can be avoided by making \( T_w < \Delta t \) (which is hard to control), by using edge-triggered Master-Slave JK flip-flops, or by using a differentiator circuit to make the clock width extremely small.

Step 4: Final Answer:
The race-around condition occurs when the clock pulse width is greater than the propagation delay of the flip-flop (\( T_w > \Delta t \)).