Question

Calculate the full scale output value of an 8-bit DAC for the 0 to 10 V range?

• A. \(0.039~V\)
• B. \(5~V\)
• C. \(9.961~V\)
• D. \(10~V\)

Hint:

For an \(n\)-bit DAC, \[ V_{FS} = \left(1-\frac{1}{2^n}\right)V_{ref} \] which is always slightly less than the reference voltage.

Answer 1

The Correct Option is C

Concept: For an \(n\)-bit DAC, \[ \text{Full Scale Output} = \left(\frac{2^n-1}{2^n}\right)V_{ref} \] because the maximum digital input is \[ (11111111)_2=(2^8-1)=255. \]

Step 1: Write the given data.
\[ n=8 \] \[ V_{ref}=10V \]

Step 2: Apply the full-scale output formula.
\[ V_{FS} = \left(\frac{255}{256}\right)\times10 \] \[ = 9.9609375V \]

Step 3: Approximate the result.
\[ V_{FS}\approx9.961V \] \[ \boxed{V_{FS}=9.961V} \]