Question

mod-64 ripple counter can be designed using 
 

• A. 4
• B. 5
• C. 6
• D. 7

Hint:

For any MOD-\(N\) counter, number of flip-flops required is \( n = \log_2 N \). If \(N\) is a power of 2, simply find the exponent.

Answer 1

The Correct Option is C

Step 1: Understanding the Question 
The question asks for the number of flip-flops required to construct a MOD-64 ripple counter. A MOD-N counter is a counter that has N distinct states, typically counting from 0 to N-1.
Step 2: Key Formula or Approach 
The number of distinct states (N) that a counter can have is related to the number of flip-flops (n) it contains. Since each flip-flop has two states (0 and 1), n flip-flops can represent a total of $2^n$ unique states. For a ripple counter that counts through its full natural sequence, the relationship is: \[ N = 2^n \] To find the required number of flip-flops, we need to solve this equation for n.
Step 3: Detailed Explanation 
We are given that the counter is a MOD-64 counter, so N = 64.
We substitute this value into our formula:
\[ 64 = 2^n \] To find n, we can express 64 as a power of 2.
We know that: 
 $2^1 = 2$
 $2^2 = 4$ 
 $2^3 = 8$ 
 $2^4 = 16$ 
 $2^5 = 32$ 
 $2^6 = 64$ 

 Therefore, we can see that $n = 6$.
Step 4: Final Answer 
A MOD-64 ripple counter requires 6 flip-flops to be designed. This corresponds to option (3).