Discussion
The tpd for each flip-flop is 50ns, determine the maximum operating frequency for MOD-32 ripple counter :
Answer: A
The maximum operating frequency is 4 MHz.
A MOD-32 counter needs 5 flip-flops, since \(2^5 = 32\). In a ripple counter each flip-flop is clocked by the one before it, so in the worst case the delays add up before the count settles:
\[ \begin{aligned} t_{total} &= 5 \times 50\ \text{ns} = 250\ \text{ns} \\ f_{max} &= \frac{1}{250\ \text{ns}} = 4\ \text{MHz} \end{aligned} \]
4 GHz is the same digits with the wrong prefix. 3 MHz and 2 MHz match no sensible count of flip-flops: 2 MHz would need ten flip-flops' delay, which is a MOD-1024 counter.
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