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 required for a MOD-N counter is given by the formula: \[ N = 2^n \quad \text{where} \quad n \text{ is the number of flip-flops.} \] For MOD-31, we need to find \( n \) such that \( 2^n \geq 31 \).

Step 2: Calculate the number of flip-flops.
Since \( 2^5 = 32 \) and \( 2^4 = 16 \), the smallest \( n \) for which \( 2^n \geq 31 \) is \( n = 5 \). Thus, the number of flip-flops required for MOD-31 is 5.
Final Answer: \[ \boxed{5} \]