Question

The number of flip-flops required to implement a MOD-31 counter are:

• A. 25
• B. 5
• C. 12
• D. 24

Hint:

For a MOD-N counter, the number of flip-flops is determined by the smallest \( n \) such that \( 2^n \geq N \).

Answer 1

The Correct Option is B

Step 1: Understanding the MOD counter.
The number of flip-flops, \( n \), needed for a MOD-N counter is determined by: \[N = 2^n \quad \text{where} \quad n \text{ is the number of flip-flops.}\]For a MOD-31 counter, we must find the smallest \( n \) satisfying \( 2^n \geq 31 \).

Step 2: Calculate the number of flip-flops.
Since \( 2^5 = 32 \) and \( 2^4 = 16 \), the minimum value of \( n \) such that \( 2^n \geq 31 \) is \( n = 5 \).Therefore, a MOD-31 counter requires 5 flip-flops.
Final Answer: \[\boxed{5}\]