Cascading counters — overall modulus calculation When two digital counters are cascaded (one drives the next), the overall MOD (modulus) of the combined counter is equal to the ________ of their individual MOD numbers.

Introduction / Context:
Counters are sequential circuits that step through a fixed number of states, known as the MOD or modulus. In practical designs we often cascade counters to obtain large divide ratios (for example, frequency dividers in timing circuits). Understanding how the overall modulus combines when counters are connected in series is a foundational skill in digital electronics and clock-generation design.

Given Data / Assumptions:

• Two counters are cascaded so that the terminal count (or ripple output) of the first counter drives the clock/enable of the second.
• Each counter has a well-defined modulus: MOD_A and MOD_B.
• No skipped states or special decoding are introduced other than standard cascading.

Concept / Approach:

When counters are cascaded, the second counter advances once for every complete cycle of the first. Therefore, the total number of unique states before the overall system repeats is the number of states in the first counter multiplied by the number of states in the second. This is analogous to a base-N odometer where one wheel increments only after the lower wheel completes a full revolution.

Step-by-Step Solution:

Verification / Alternative check:

Example: cascade a MOD-10 (decade) with a MOD-6 counter to form a minutes counter (seconds → minutes). The total modulus is 10 * 6 = 60, matching the 00–59 range. This simple cross-check demonstrates the multiplicative rule.

Why Other Options Are Wrong:

Sum: would imply the system repeats after MOD_A + MOD_B pulses, which contradicts the odometer behavior.

Log: bears no relation to state counting.

Reciprocal: has no meaning in this discrete-state context.

Common Pitfalls:

Confusing synchronous gating with asynchronous ripple; forgetting that decode/reset logic can change the effective modulus (but the basic cascade without extra decoding multiplies). Also, ensure the cascade uses appropriate enables or ripple outputs to avoid missed counts.

Final Answer:

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