In digital timekeeping applications, which systems most commonly employ mod-6 and mod-12 counters for dividing and displaying time?

Introduction / Context:
Time displays rely on dividing a reference frequency into human-readable units. Modulus counters (counters that reset after reaching a fixed count) are arranged to implement decimal or sexagesimal divisions. Mod-6 and mod-12 counters are classic building blocks for hours and seconds/minutes displays in clocks.

Given Data / Assumptions:

• Seconds and minutes are base-60 (6×10) systems.
• Hours are often displayed in 12-hour format.
• Counters receive a known clock (e.g., 1 Hz derived from a crystal).

Concept / Approach:
A mod-10 counter cycles 0–9; cascading a mod-6 and a mod-10 yields 0–59 for seconds/minutes. For hours, a mod-12 counter cycles 1–12 (often implemented as 0–11 then converted). These modulus values map neatly onto the conventional time base used by digital clocks, and decoder/driver circuits feed seven-segment displays.

Step-by-Step Solution:
Derive 1 Hz from a crystal (e.g., 32.768 kHz divided by 2^15).Use mod-10 for units of seconds and a following mod-6 for tens of seconds to reach 60 states.Repeat the mod-6/mod-10 pair for minutes.Use a mod-12 counter to track hours in 12-hour format, with AM/PM toggle.

Verification / Alternative check:
Common digital clock ICs and reference designs show exactly these division chains, confirming the prevalence of mod-6 and mod-12 counters in clock applications.

Why Other Options Are Wrong:

• Frequency counters: Typically use binary or decade counters but not specifically mod-6 and mod-12 combinations.
• Multiplexed displays: A display driving technique, not a counting modulus choice.
• Power meters / PWM: Use different counting/control strategies unrelated to 12- or 60-based time divisions.

Common Pitfalls:

• Mistaking mod-60 as a single counter; it is usually realized by mod-6 and mod-10 cascades.
• Forgetting display decoding for leading zero suppression or 12→1..12 mapping.

Final Answer:
digital clocks