Frequency counter design math: dividing a 100 kHz system clock to 1 Hz A frequency counter uses a 100 kHz system clock as its timing reference. How many cascaded decade (/10) counters are required to obtain an accurate 1 Hz timing signal?

Introduction / Context:
Gate-time generation is central to frequency counters. If the system clock is 100 kHz, the designer must divide it down to 1 Hz to define a 1-second measurement interval. Decade counters are a common HDL-friendly choice for divisions by powers of ten.

Given Data / Assumptions:

• System clock f_sys = 100 kHz.
• Target gate frequency f_gate = 1 Hz.
• Available blocks: decade (/10) counters.

Concept / Approach:
To go from 100,000 Hz to 1 Hz requires an overall division of 100,000. Using only /10 counters, we need N such that 10^N = 100,000.

Step-by-Step Solution:

Verification / Alternative check:
Simulation: observe one output rising edge per 100,000 input cycles; period = 1 s at 100 kHz input.

Why Other Options Are Wrong:

• 6: Would divide to 0.1 Hz (10 seconds period).
• 4: Divides to 10 Hz.
• 3: Divides to 100 Hz.

Common Pitfalls:
Mixing decimal and binary divisors; be consistent with chosen counter modulus.

Final Answer:
5