Cascading decade counters Four cascaded modulus-10 (decade) counters together will produce what overall modulus?

Introduction / Context:Counters are often cascaded to extend the range of counting. When you cascade counters, the total modulus is the product of the individual moduli, enabling decimal timekeeping and event-counting over large ranges using standard decade devices.

Given Data / Assumptions:

• Each stage: modulus 10.
• Number of stages: 4 (units, tens, hundreds, thousands).
• Proper cascading: carry (or ripple) from one stage clocks the next.

Concept / Approach:The overall modulus of cascaded counters equals the product of their individual moduli. Therefore, four decades produce 10 * 10 * 10 * 10 = 10,000 unique states before the sequence repeats. This principle generalizes to any set of cascaded counters with possibly different moduli (overall modulus = product of all).

Step-by-Step Solution:

Verification / Alternative check:Observe a 4-digit decimal counter: units advances each pulse; tens advances each time units rolls over; and so on—clearly yielding 10,000 states.

Why Other Options Are Wrong:

• 10, 100, 1,000: These are products for 1, 2, and 3 cascaded decades respectively.

Common Pitfalls:Miscounting the number of stages; failing to ensure proper carry/ripple connections so that the theoretical modulus is actually realized in hardware.

Final Answer:10,000