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For synchronous series counter of modulus 256, the propagation delay for each flip flop is 25 nsec and propagation delay of each two input AND gate is 5 nsec. What is the maximum frequency of the MOD256 counter ? (in MHz)
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This is a 4-bit Synchronous Binary Up Counter

Here, each Flip flop get clock pulse at the same time. So, when the clock is applied, in 25 nsec all 4 flip-flop will give output + we need inputs for the next stage of flip-flops so additional 5 nsec + 5 nsec (two AND gates) will be needed. So, minimum time period needed for clock is 25 + 5 + 5 = 35 nsec.

According to ques. for MOD-256 counter we need 8 flip-flops
$\therefore$ we need (8-2) AND gates in series connection (as mentioned two input AND gates only) 

$F\_{clk}$ $= \frac{1}{T_{FF} + (8-2) T_{gate}}\\ = \frac{1}{25 + (8 -2) 5 }\\ = 0.01818 \times 10^{9}\\ = 18.18\ \ MHZ$

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Propagation Delay for Synchronous counter does not depend on the no of flip flops because in sychronous counter clock is applied to each flip flop at the same time .

so Propagation delay of Synchronous counter = Propagation delay of Flip flop + delay due to combination circuit

                                                                  = 25 nsec + 5 nsec =30 nsec

So frequency = 1/ Time period = 1/30ns =33.33 MHZ


Not exact duplicate question ;- https://gateoverflow.in/26442/gate1991_5-c

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Mod ≤ 2
256 ≤ 2n 
n=8 flip-flops 

Total delay of Synchronous series counter = Tpd(Flipflop) + (n-2)Tpd(AND gate)

=25ns + (8-2) 5ns = 25 + 30 = 55 ns
Frequency of synchronous series counter 

Frequency =1/Total delay = 1/55ns =  18.18 MHz

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