Understanding 4-Digit Digital Instrument Resolution

The resolution of a digital measuring instrument refers to the smallest change in the measured value that the instrument can detect and display. It is determined by the number of digits or counts that the instrument can display.

In a digital instrument, the display shows a numerical value. The number of digits indicates the maximum count the instrument can register. A standard interpretation of a "4-digit" instrument implies that it can display values from 0 up to 9999. This means the instrument has a total of 10000 possible counts (from 0000 to 9999).

The resolution is typically defined by the value represented by the least significant digit (the rightmost digit). For an instrument with 10000 counts, the smallest change it can display is 1 count.

To express the resolution as a percentage of the full scale, we use the following formula:

\( \text{Resolution (\% of full scale)} = \left( \frac{\text{Smallest detectable change}}{\text{Full scale value (maximum counts)}} \right) \times 100\% \)

For a 4-digit instrument displaying up to 9999:

• Smallest detectable change = 1 count
• Full scale value (maximum counts) = 10000 counts (representing a range from 0 to 9999)

Let's calculate the resolution:

\( \text{Resolution (\%)} = \left( \frac{1}{10000} \right) \times 100\% \)

\( \text{Resolution (\%)} = 0.0001 \times 100\% \)

\( \text{Resolution (\%)} = 0.01\% \)

This calculation shows that the resolution for a 4-digit digital measuring instrument, based on a 10000-count range, is 0.01% of the full scale.

Comparing this result with the given options:

• 0.002%
• 0.005%
• 0.1%
• 0.01%

The calculated resolution matches the option 0.01%.

Therefore, the resolution of a 4-digit digital measuring instrument, interpreted as having a 10000-count capability, is 0.01%.