Overall modulus of cascaded decade counters: Evaluate the statement: “Three cascaded modulus-10 (decade) counters yield an overall modulus of 1000.”

Introduction / Context:
Understanding how counter moduli combine is essential when building frequency dividers, timers, or decimal displays. When counters are cascaded, their overall modulus is the product of the individual moduli, provided they are chained conventionally (carry/ripple from the lower decade drives the next).

Given Data / Assumptions:

• Three decade (mod-10) counters are cascaded.
• Standard ripple or synchronous cascading is used with proper carry chaining.
• No additional gating is introduced to alter the count length.

Concept / Approach:
The overall modulus M_total of cascaded counters equals the product of the individual moduli. For three mod-10 stages: M_total = 10 * 10 * 10 = 1000. This results in a divide-by-1000 frequency division and a 000 to 999 counting range for display applications.

Step-by-Step Solution:

Verification / Alternative check:
Observe a three-digit decimal display driven by cascaded decade counters; it cycles from 000 to 999. Frequency measurement confirms the input is divided by 1000 at the most significant stage output.

Why Other Options Are Wrong:

• Incorrect: Contradicts the multiplicative property of cascaded moduli.
• Only if synchronous / Only if clock is 1 kHz / Depends on load capacitance: Timing style and frequency do not change the count length; loading affects speed, not modulus.

Common Pitfalls:
Miswiring carry outputs so the chain fails to propagate; adding gating that truncates counts (creating non-10 moduli) and then forgetting the overall modulus changes accordingly.

Final Answer:
Correct