GATE 2020 IN Q.43: solution and answer

GATE 2020 · INQ.43 · 2 marks · NAT

A $6 \frac{1}{2}$ digit timer-counter is set in the 'time period' mode of operation and the range is set as 'ns'. For an input signal, the timer-counter displays 1000000. With the same input signal, the timer-counter is changed to 'frequency' mode of operation and the range is set as 'Hz'. The display will show the number ____

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Answer and solution

ANSWER

The display shows 1000, because the period is 1000000 ns = 1 ms and the frequency is 1/(1 ms) = 1000 Hz.

Official answer: 999 to 1001Source: Official answer key, GATE 2020 IN (IIT Delhi)

In period mode the display gives the period as a count in the selected unit. With the range at ns, the period is $T = 1000000 ns$ .
Convert to seconds: $T = 1 0^{6} \times 1 0^{- 9} s = 1 0^{- 3} s = 1 ms$ .
The input signal has not changed, and frequency is the reciprocal of period: $f = \frac{1}{T} = \frac{1}{1 0 ^{- 3} s} = 1000 Hz$
In frequency mode with the range at Hz, the display gives the frequency in hertz, so it reads $1000$ . That fits easily on a $6 \frac{1}{2}$ digit display, which can show up to $1999999$ .

KEY IDEA

A timer-counter shows its reading as a number in the selected range unit. Turn the period reading into seconds, take the reciprocal to get the frequency, then write that frequency in the new range unit (Hz).

WATCH OUT FOR

Using the displayed number without its unit and writing $f = 1/1 0^{6} = 1 0^{- 6}$ . Another error is treating ns as $1 0^{- 6} s$ (that is microseconds), which gives 1 Hz. The reading $1 0^{6} ns$ is $1 0^{- 3} s$ , so the frequency is $1000 Hz$ .

From the GATE 2020 IN paper. Every question of this paper · Download the full paper · All 5 Time, frequency & scopes questions, with notes

GATE 2020 IN Q.43: solution and answer

Answer and solution

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