GATE 2026 IN – Question 62
A digital counter increments its count every $0.1\ \mu\mathrm s$. The counter is used in an instrument to measure frequency. It is operated for one period of the input signal. The input signal is approximately at 100 kHz. The maximum error in the measured frequency is ________ kHz. (Rounded off to the nearest integer.)
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Correct answer: 1 to 1
Explanation
The input period is $T=1/(100\ \mathrm{kHz})=10\ \mu\mathrm s$. A one-count uncertainty corresponds to $\Delta T=0.1\ \mu\mathrm s$, or 1% of the period.
Since $f=1/T$, the first-order error is $|\Delta f|\approx f\Delta T/T=1\ \mathrm{kHz}$. Direct inversion at $T-\Delta T=9.9\ \mu\mathrm s$ gives the larger deviation, about 1.01 kHz, which also rounds to **1 kHz**.