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How many flip-flops are needed to divide the input frequency by 40?
1. 4
2. 5
3. 6
4. 40

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Correct Answer - Option 3 : 6

Concept:

A MOD-N counter is also called a divide by N counter as the input frequency is divided by the number of states of the counter.

For a counter with ‘n’ flip flops:

  • The total number of states = 2n (0 to 2n – 1)
  • The largest number that can be stored in the counter = 2n – 1

 

To construct a counter with any MOD number, the minimum number flip flops required must satisfy:

Modulus ≤ 2n

Where n is the number of flip-flops and is the minimum value satisfying the above condition.

Calculation:

We are required to construct a counter which divides the input frequency by 40, i.e. we require a MOD-40 counter.

Number no. of flip – flops are required to construct mod-40 counter, must satisfy:

2≥  40

The minimum value of n satisfying the above is:

n = 6 bits

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