Digital clock project — identify the three basic counter blocks When implementing a 12-hour digital clock from counters, which set of counter moduli represents the three basic building blocks used to form the seconds, minutes, and hours counts?

Introduction / Context:
A digital clock divides time into seconds, minutes, and hours. Practical hardware uses cascaded modulus counters to realize the decimal-looking outputs needed for display. Understanding which moduli are required keeps the design minimal and modular, simplifying debugging and reuse.

Given Data / Assumptions:

• Seconds and minutes each count 0–59.
• Hours (12-hour format) count 1–12 (or 0–11 internally).
• BCD displays prefer decade-based counters for easy digit driving.

Concept / Approach:
To get 0–59, hardware commonly uses a MOD-10 counter for the ones digit (0–9) and a MOD-6 counter for the tens digit (0–5). Chaining these two yields MOD-60. For hours in a 12-hour clock, a MOD-12 counter is used (often realized as a decade counter with additional logic or a dedicated MOD-12). Thus, the fundamental building blocks are MOD-10, MOD-6, and MOD-12.

Step-by-Step Solution:

Verification / Alternative check:
Many textbooks and lab kits implement seconds/minutes using a 7490/4510 decade counter feeding a 7492/4511 MOD-6 stage; hours use a MOD-12 realized with gating or a dedicated counter, confirming the chosen set.

Why Other Options Are Wrong:

• Option a/c: omit one needed modulus; you need three building blocks.
• Option b: MOD-5 is not used; tens digit must roll 0–5, not 0–4.
• Option e: arbitrary moduli unrelated to clock division.

Common Pitfalls:

• Confusing “final modulus” (60) with the underlying cascaded moduli (10 and 6).

Final Answer:
MOD-6, MOD-12, and MOD-10 counters