Cascade division calculation A MOD-12 counter is cascaded with a MOD-10 counter. If the input clock is 60 MHz, what is the resulting output frequency from the cascade?

Introduction / Context:
Cascaded counters divide an input clock by the product of their individual moduli. This is a common technique for generating precise lower-frequency time bases from a high-frequency oscillator in frequency synthesizers, digital clocks, and timing controllers.

Given Data / Assumptions:

• First stage modulus: 12.
• Second stage modulus: 10.
• Input frequency: 60 MHz.
• Assume ideal counters with no missing counts and proper cascading.

Concept / Approach:
The overall division factor equals MOD_total = MOD1 * MOD2. Therefore, the output frequency equals f_out = f_in / MOD_total. We perform a straightforward numeric substitution and a unit conversion from MHz to kHz if needed for clarity.

Step-by-Step Solution:

Verification / Alternative check:
If each counter alone divided the clock, the first would produce 5 MHz (60/12), and the second would further divide by 10: 5 MHz / 10 = 0.5 MHz, consistent with 500 kHz.

Why Other Options Are Wrong:

• 1,500 kHz: Corresponds to division by 40, not 120.
• 6 MHz: Division by 10 only, ignoring the MOD-12 stage.
• 5 MHz: Output after only the MOD-12 stage, not the cascade.

Common Pitfalls:
Forgetting to multiply moduli in series; confusing MHz and kHz; or mis-ordering the cascade (order does not affect the product result).

Final Answer:
500 kHz