Mod-10 Asynchronous Counter

To understand why option C is the correct answer, we first need to understand what a mod-10 asynchronous counter is and how it works.

What is a Mod-10 Asynchronous Counter?

A mod-10 asynchronous counter is a type of digital counter that counts in binary from 0 to 9 and then repeats the counting sequence. It is called asynchronous because the flip-flops in the counter change state independently of a clock signal.

How does a Mod-10 Asynchronous Counter work?

A mod-10 asynchronous counter can be implemented using T flip-flops. Each T flip-flop represents a binary bit, and the counter advances by 1 with each clock pulse. When the count reaches 9, the next clock pulse causes the counter to reset to 0.

To implement a mod-10 asynchronous counter, we need to determine the number of T flip-flops required.

Calculating the Number of T Flip-Flops

To determine the number of T flip-flops required, we need to consider the number of states in the counter. Since a mod-10 counter counts from 0 to 9 (10 states), we need a total of 10 flip-flops.

However, we can reduce the number of flip-flops required by using a technique called state reduction. In this technique, we group together states that have the same output and combine them into a single state. This reduces the number of flip-flops required without affecting the functionality of the counter.

In the case of a mod-10 counter, we can observe that the states 0 and 10 have the same output. Similarly, states 1 and 11, states 2 and 12, and so on, all have the same output. By combining these states, we can reduce the number of states from 20 to 10.

Therefore, the number of T flip-flops required to realize a mod-10 asynchronous counter is 10.

Conclusion

In conclusion, the correct answer is option C, which states that 4 T flip-flops are required to realize a mod-10 asynchronous counter. The number of flip-flops required can be reduced by using state reduction techniques, but the minimum number of flip-flops required to implement a mod-10 counter is 4.