Compute the divided clock frequency A digital counter chain divides a 4 MHz input clock by an overall factor of 5000 before presenting the labeled output. Determine the resulting output frequency.

Introduction / Context: Many timing applications derive a lower-frequency clock from a high-frequency source by cascading divide-by-N counters. The output frequency is computed by dividing the input by the total modulus.

Given Data / Assumptions:

• Input clock frequency f_in = 4 MHz.
• Total division factor N = 5000.
• Output frequency f_out = f_in / N.

Concept / Approach: Use the simple frequency division relationship. Ensure units are consistent (hertz). Avoid common mistakes such as multiplying or misreading the modulus.

Step-by-Step Solution:

Verification / Alternative check: Break the factor into 100 * 50: 4 MHz / 100 = 40 kHz; 40 kHz / 50 = 800 Hz, confirming the same result.

Why Other Options Are Wrong: “4 MHz” implies no division. “20 kHz” would correspond to a 200 division. “210.5 kHz” is unrelated to an integer divide of 5000.

Common Pitfalls: Mixing kHz and Hz or dropping zeros; always track powers of ten carefully in frequency division problems.

Final Answer: 800 Hz