Question

How would a binary number 0010 be represented by a 4-bit binary word, if the range of voltage is 0 to 10 V?
1. 0.666 V
2. 1.333 V
3. 0.333 V
4. 2.000 V

Answer 1

Correct Answer - Option 2 : 1.333 V

Concept:

Output voltage of DAC is calculated as:

Output voltage = decimal equaled × Resolution

Resolution: It is defined as the smallest change in the analog output voltage corresponding to a change of one bit in the digital output.

The percentage resolution (R) of an n-bit DAC is given as:

 \(R = \frac{1}{{{2^n} - 1}} \times 100\)

The resolution of an n-bit DAC with a range of output voltage from 0 to V is given by:

Resolution = \(\frac{{{V_{FS}}}}{{{2^n} - 1}}\) 

Calculations:

Given:

V_FS = 10V

n = 4

(0010)₂ →  (2)₁₀

Resolution = \(\frac{{10}}{{{2^4} - 1}} = 0.6667\)

Output voltage = (0.6667) × 2

Output voltage = 1.333 V