Explanation:
To understand why the final output of three T flip-flops in a cascade is 12.5 MHz, let's first understand what a T flip-flop does and how it works.

T Flip-Flop:
A T flip-flop is a type of flip-flop that toggles its output based on the input signal. The input to a T flip-flop is called the "toggle" input, and it can either be a logic high (1) or a logic low (0). When the toggle input is high (1), the output of the flip-flop toggles between its current state and its complemented state. When the toggle input is low (0), the output remains unchanged.

Cascade Connection:
When multiple flip-flops are connected in cascade, the output of one flip-flop becomes the input to the next flip-flop. In this case, we have three T flip-flops connected in cascade.

Frequency Division:
Each T flip-flop in the cascade divides the input frequency by two. This means that the output frequency of the first flip-flop is half of the input frequency, the output frequency of the second flip-flop is half of the output frequency of the first flip-flop, and so on.

Calculating the Output Frequency:
Given that the input frequency is 100 MHz, let's calculate the output frequency of the cascade.

- The output frequency of the first flip-flop is half of the input frequency, which is 100 MHz / 2 = 50 MHz.
- The output frequency of the second flip-flop is half of the output frequency of the first flip-flop, which is 50 MHz / 2 = 25 MHz.
- The output frequency of the third flip-flop is half of the output frequency of the second flip-flop, which is 25 MHz / 2 = 12.5 MHz.

Therefore, the final output of the three T flip-flops in a cascade is 12.5 MHz.

Conclusion:
The final output of three T flip-flops in a cascade, when the input is a 100 MHz signal, is 12.5 MHz. This is because each flip-flop divides the frequency by two, resulting in a progressive reduction of the frequency as it passes through each flip-flop.