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: Thinking in terms of binary counting. 
A digital counter made using flip-flops actually counts in binary. Each additional flip-flop adds one more binary digit (bit) to the count.

Step 2: States produced by binary bits.
With binary counting:
\[ 1 \text{ flip-flop } \rightarrow 2 \text{ states} \]
\[ 2 \text{ flip-flops } \rightarrow 4 \text{ states} \]
\[ 3 \text{ flip-flops } \rightarrow 8 \text{ states} \]
\[ 4 \text{ flip-flops } \rightarrow 16 \text{ states} \]

Step 3: Matching states with MOD-10 requirement.
A MOD-10 counter must count from 0 to 9, which requires exactly 10 states.
Binary counting with 3 flip-flops stops at 8 states, which is insufficient.
Binary counting with 4 flip-flops reaches 16 states, which comfortably includes 10 required states.

Step 4: Handling extra states.
The extra states (10 to 15) are simply skipped or reset using additional logic, while the counter cycles through 0 to 9 only.

Final Conclusion:
Since 4 flip-flops provide enough binary combinations to include 10 counting states, a MOD-10 counter requires 4 flip-flops.