Cascaded MOD-5 counters — overall counting range Three counters, each with modulus 5 (MOD-5), are cascaded in series. What is the overall modulus (maximum unique count before the sequence repeats)?

Introduction / Context:
Cascading digital counters multiplies their individual moduli. This question checks whether you can determine the total counting range when multiple modulus-N stages are chained, a common design in timing dividers and sequence generators.

Given Data / Assumptions:

• There are three cascaded counters.
• Each counter is modulus 5 (counts 0 through 4 and then rolls over).
• The counters are connected so that the overall count cycles through every unique combination.

Concept / Approach:
When counters are cascaded such that one stage advances the next on overflow, the total modulus equals the product of the individual moduli. Thus, MOD-A followed by MOD-B yields MOD-(A*B); extend this by multiplication for more stages.

Step-by-Step Solution:

Verification / Alternative check:
List the ranges: the least significant stage has 5 states; for each of those, the second has 5; for each pair, the third has 5. That is 5 * 5 * 5 = 125 unique combinations before repeating.

Why Other Options Are Wrong:

• 5: would be a single MOD-5 stage only.
• 25: corresponds to two MOD-5 stages (5 * 5).
• 500: not a power-of-5 product from three MOD-5 counters.

Common Pitfalls:
Adding moduli instead of multiplying; forgetting that each additional cascaded stage multiplies total states.

Final Answer:
125