Digital clock HDL design: In the provided digital clock project, the MOD-12 counting function (for hours) is realized using which arrangement of simpler counters?

Introduction / Context:
Clock projects often decompose timekeeping into smaller counters for seconds, minutes, and hours. Implementing MOD-12 for 12-hour time is a classic exercise in counter composition. Designers frequently realize composite moduli by cascading smaller modulus counters whose product equals the target modulus, adding gating logic as needed for irregular ranges (such as 1–12 vs. 0–11).

Given Data / Assumptions:

• Goal: count 12 distinct states for hours.
• Standard cascading rule: overall modulus = product of individual moduli.
• Simple educational decomposition uses MOD-6 and MOD-2.

Concept / Approach:
By cascading a MOD-6 counter (producing six states) with a MOD-2 counter (producing two states), we get an overall modulus of 12. Additional decode/translate logic may be used to map internal states to human-friendly hour digits (1–12) and to handle rollovers (e.g., 11 → 12 → 1). This approach keeps counter design simple and reuses well-known blocks.

Step-by-Step Solution:

Verification / Alternative check:
Simulation validates a 12-state sequence before rollover. The hour display transitions 11 → 12 → 1 with the proper AM/PM toggle logic elsewhere in the design.

Why Other Options Are Wrong:

• BCD+MOD-2: BCD is MOD-10; 10*2=20, not 12.
• Single HDL module: Possible, but the question focuses on decomposition.
• MOD-12 plus a DFF: The DFF is unnecessary for modulus composition.
• Two MOD-4 counters: 4*4=16, not 12.

Common Pitfalls:
Forgetting that 12-hour format displays 1–12 rather than 0–11; failing to implement the 11→12→1 mapping; neglecting AM/PM flip-flop control at rollover.

Final Answer:
A MOD-6 counter followed by a MOD-2 counter