Question 44 In a 4 Bit Ripple counter, JK flip flops are used.
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Question 44
In a 4 Bit Ripple counter, JK flip flops are used. If the propagation delay of each JK Flip Flop is 8 ns, what will be the worst case propagation delay for the 4 Bit Ripple Counter?
Show answer & explanation
In a ripple counter, each flip-flop's output drives the clock input of the next flip-flop in sequence. The worst-case propagation delay occurs when a carry ripples through all stages. With 4 flip-flops and 8 ns per stage, the maximum delay is 4 × 8 = 32 ns. Options B (40 ns) and D (16 ns) use incorrect multipliers, and C (8 ns) ignores the cascading effect.
Step-by-step Derivation:
Ripple Counter Worst-Case Propagation Delay Calculation:
Structure: In a 4-bit ripple counter, flip-flops are connected in cascade:
- FF₀ (LSB) counts directly from input clock
- FF₁'s clock = FF₀'s output
- FF₂'s clock = FF₁'s output
- FF₃'s clock = FF₂'s output
Worst-Case Scenario: When all flip-flops need to toggle (e.g., counting from 0111 to 1000), the carry ripples through all 4 stages sequentially.
Propagation Path:
- FF₀ toggles after 8 ns
- FF₁ toggles after FF₀'s output is stable: 8 + 8 = 16 ns
- FF₂ toggles after FF₁'s output is stable: 16 + 8 = 24 ns
- FF₃ toggles after FF₂'s output is stable: 24 + 8 = 32 ns
Formula: tpd_total = n × tpd_per_stage
where n = number of stages (4), tpd_per_stage = 8 ns
tpd_total = 4 × 8 = 32 ns
Answer: A) 32 ns