Converting period to frequency for a digital clock If a clock waveform has a period of 1.25 µs, what is the corresponding frequency in hertz?

Introduction / Context:
Clock specification conversions between period (time per cycle) and frequency (cycles per second) are routine in digital design, timing analysis, and interface selection.

Given Data / Assumptions:

• Clock period T = 1.25 microseconds.
• Frequency f = 1 / T.
• Unit conversions: 1 µs = 10^-6 s.

Concept / Approach:

The inverse relationship f = 1/T directly gives frequency once the period is expressed in seconds. Carefully convert microseconds to seconds to avoid thousand- or million-fold mistakes.

Step-by-Step Solution:

Verification / Alternative check:

Check scale: a period near 1 µs corresponds to near 1 MHz. At 1.25 µs, the frequency should be slightly less than 1 MHz, consistent with 0.8 MHz.

Why Other Options Are Wrong:

• 8 kHz / 0.8 kHz: off by factors of 10^2–10^3 due to incorrect microsecond conversion.
• 8 MHz: corresponds to a 0.125 µs period, not 1.25 µs.
• 12.5 MHz: corresponds to 0.08 µs, far smaller period.

Common Pitfalls:

• Mixing micro (10^-6) with milli (10^-3).
• Inverting incorrectly: using f = T instead of f = 1/T.

Final Answer:

0.8 MHz