Question

How many flip-flops are required to design a MOD-10 counter?

• A. 3
• B. 4
• C. 5
• D. 10

Hint:

To design a MOD-N counter, always choose the smallest n such that \(2^n \geq N\).

Answer 1

The Correct Option is B

Step 1: Understanding a MOD counter.
A MOD-N counter is a digital counter that goes through N distinct states before repeating the counting sequence. A MOD-10 counter must count from 0 to 9, which means it requires 10 unique states.
Step 2: Relation between number of states and flip-flops.
The number of states that can be represented using n flip-flops is given by:
\[ 2^n \] We must choose the smallest value of n such that \( 2^n \geq 10 \).
Step 3: Calculating the required number of flip-flops.
\[ 2^3 = 8 \quad (\text{not sufficient})
2^4 = 16 \quad (\text{sufficient}) \] Thus, a minimum of 4 flip-flops is required to represent at least 10 states.
Step 4: Conclusion.
Since 4 flip-flops can represent up to 16 states, they are sufficient to design a MOD-10 counter.