GATE EC 2020 Set 1 — Question 30
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Digital Circuits → Data Converters → DAC (Weighted, R-2R)
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Question
A 10-bit D/A converter is calibrated over the full range from 0 to 10 V. If the input to the D/A converter is 13A (in hex), the output (rounded off to three decimal places) is ________ V.
Correct answer
3.05 to 3.08
Solution
Step 1: Convert the hexadecimal input to decimal.
Input .Step 2: Calculate the output voltage.
For a 10-bit DAC, the number of steps is (or depending on convention; GATE range accepts both).
Using :
V_{out} = rac{ ext{Digital Input}}{2^n - 1} imes V_{FS} = rac{314}{1023} imes 10 \approx 3.0694 ext{ V}.
Using :
V_{out} = rac{314}{1024} imes 10 \approx 3.0664 ext{ V}.
Both values fall within the range . Rounded to three decimal places, we get or .
Input .Step 2: Calculate the output voltage.
For a 10-bit DAC, the number of steps is (or depending on convention; GATE range accepts both).
Using :
V_{out} = rac{ ext{Digital Input}}{2^n - 1} imes V_{FS} = rac{314}{1023} imes 10 \approx 3.0694 ext{ V}.
Using :
V_{out} = rac{314}{1024} imes 10 \approx 3.0664 ext{ V}.
Both values fall within the range . Rounded to three decimal places, we get or .
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