This question asks us to compare the worst-case delay of a 4-bit ripple counter and a 4-bit synchronous counter, given that each flip-flop used has a propagation delay of 10 ns.

Ripple Counter Worst-Case Delay Calculation (R)

A ripple counter, also known as an asynchronous counter, connects flip-flops in a serial manner. The output of one flip-flop serves as the clock input for the next flip-flop. This sequential clocking means that the clock signal (or the change in output) effectively 'ripples' through the counter.

For a 4-bit ripple counter, there are 4 flip-flops. The total worst-case delay occurs when the last flip-flop changes its state based on the output change from the first flip-flop. This delay is the sum of the propagation delays of all the flip-flops in the chain.

• Propagation delay per flip-flop = $10 \text{ ns}$
• Number of flip-flops = 4

Therefore, the worst-case delay for the ripple counter (R) is calculated as:

$$ R = \text{Number of flip-flops} \times \text{Propagation delay per flip-flop} $$ $$ R = 4 \times 10 \text{ ns} $$ $$ R = 40 \text{ ns} $$

Synchronous Counter Worst-Case Delay Calculation (S)

In a synchronous counter, all flip-flops are triggered simultaneously by a common clock signal. The next state of each flip-flop is determined by the current state and the counter's logic (e.g., using AND gates to control the clock enable or J-K inputs).

Since all flip-flops receive the clock pulse at the same time, the delay associated with the clock triggering is the delay of a single flip-flop. The time it takes for the counter to transition to the next state is primarily limited by the time it takes for any single flip-flop to change its output after the clock edge arrives and its inputs are stable.

For a 4-bit synchronous counter, the worst-case delay (S) is determined by the propagation delay of a single flip-flop because all flip-flops change state almost simultaneously after the clock pulse.

• Propagation delay per flip-flop = $10 \text{ ns}$

Therefore, the worst-case delay for the synchronous counter (S) is:

$$ S = \text{Propagation delay per flip-flop} $$ $$ S = 10 \text{ ns} $$

Conclusion

Based on the calculations:

• Worst-case delay for the 4-bit ripple counter (R) = $40 \text{ ns}$
• Worst-case delay for the 4-bit synchronous counter (S) = $10 \text{ ns}$

This corresponds to the option stating R = 40 ns and S = 10 ns.