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?
Digital Electronics
Signals and Switches
Difficulty: Easy
Choose an option
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A8 kHz
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B0.8 kHz
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C0.8 MHz
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D8 MHz
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E12.5 MHz
Answer
Correct Answer: 0.8 MHz
Explanation
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:
T = 1.25 µs = 1.25 × 10^-6 sf = 1 / T = 1 / (1.25 × 10^-6) HzCompute: 1 / 1.25 = 0.8; and 1 / 10^-6 = 10^6 → f = 0.8 × 10^6 HzTherefore f = 0.8 MHz.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