Correct Answer - Option 1 : 1100

__Concept:__

- Analog-to-Digital Converters (ADCs) transform an analog voltage to a binary number (a series of 1’s and 0’s).
- Then eventually to a digital number (base 10) for reading on a meter, monitor, or chart.
- The ADC resolution depends upon the number of bits used to represent the digit number.
- As the number of bits increases the resolution of an Analog to Digital Converter improves and the quantization error decreases.

**Resolution for n – bit A/D converter will be:**

\(R= \frac{V_{FS} \ \times \ (2^ib^i)}{{{2^n} - 1}}\)

Where

R = Resolution

VFS is reference voltage 'or' Full-scale voltage

n = number of bits

2^{i}b^{i} gives output voltage value.

__Calculation:__

Given:

V_{FS} = 5.8 V

n = 4

R = 05 V

\( 5= \frac{5.8 \ \times \ 2^ib^i}{{{2^{4}} - 1}}\)

\( 2^ib^i= \frac{5 \ \times \ 15}{{5.8}}\)

2ibi = 12.93 V ≈ 12 V

In bits, the output voltage will be **1100**

**Hence option (1) is the correct answer.**

**The resolution of DAC is a change in analog voltage corresponding to the LSB bit increment at the input.**

The resolution (R) is calculated as:

\( R= \frac{{{V_{FS}}}}{{{2^N} - 1}}\)

No. of levels = 2N – 1

Vr is reference voltage 'or' Full-scale voltage