The MOD number of a counter is equal to the number of complete states that a cou

Question

The MOD number of a counter is equal to the number of complete states that a counter goes through before it recycles back to its starting state. To construct a ripple counter with a MOD number X, it requires a minimum number of N FFs such that 2^N Greaterthanorequalto X. What is the maximum MOD # of a counter constructed with 6 flip-flops? (b) Counters with a MOD number larger than 16 can be created by cascading 4-bit binary counters. The MOD number is equal to the product of the individual MOD numbers. For example, a MOD 80 counter can be implemented as shown in the following figure (general block diagram, all of the wiring is not shown). What is the largest MOD counter that can be implement by cascading two 4-bit binary counters together?

Explanation / Answer

a) Given, No of Flip Flops(n) = 6

Maximum MOD value = 2n = 26 = 64 (Ans).

b) In 4-bit binary counter, there are 4 flip flops used.

Explanation: n-bit binary counter, is just like a synonym for counter with specified no of flip flops with it.

Maximum MOD for 4-bit counter =  2n = 24 = 16

As in the above example, for MOD 10 and MOD 8 cascading, which results in (10*8) MOD couter = 80 MOD counter,

hence, the largest MOD counter implemented by cascading two 4-bit binary counter = 16 * 16 = 256 MOD counter (Ans)

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