How many flip-flop circuits are needed to divide by 16?

How many flip-flop circuits are needed to divide by 16? Correct Answer Four

Concept:

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.

Note: 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.

Calculation:

Number no. of flip – flops are required to construct mod-16 counter, must satisfy:

2n ≥  16

The minimum value of n satisfying the above is:

n = 4 bits