Difficulty: Easy
Correct Answer: Correct
Explanation:
Introduction: Digital systems rely on clock waveforms to sequence operations. Two fundamental descriptors of a periodic signal are period (T) and frequency (f). This question tests the canonical relationship between them used across timing analysis and specification sheets.Given Data / Assumptions:
Concept / Approach: By definition, frequency is the number of cycles per unit time. If each cycle takes T seconds, then in one second the count of cycles is 1/T. Therefore, f = 1 / T, independent of the exact waveshape (square, sine, triangle) as long as periodicity holds.Step-by-Step Solution:
1) Let T be the duration of one full cycle.2) The number of cycles in one second is 1 divided by the cycle time: f = 1/T.3) Units check: seconds cancel, leaving hertz (s^-1).Verification / Alternative check:
Example: If T = 10 ns, then f = 1 / (10 * 10^-9) = 100 MHz, which aligns with practice.Why Other Options Are Wrong:
Incorrect: Contradicts the definitional relation f = 1/T.True only for analog clocks: Applies equally to digital clocks.True only for square waves: Shape is irrelevant; periodicity is the key.Common Pitfalls:
Mixing up angular frequency w (w = 2 * pi * f) with linear frequency f.Using milliseconds or nanoseconds without converting to seconds first.Final Answer:
Correct
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