Question

A 6-bit ADC has a maximum precision supply voltage of 20 V. What are the voltage changes for each LSB present and voltage to be presented by (100110), respectively?

1. 0.317 V and 12.06 V
2. 3.17 V and 12.06 V
3. 0.317 V and 1.206 V
4. 3.17 V and 1.206 V

Answer 1

Correct Answer - Option 1 : 0.317 V and 12.06 V

Concept:

Resolution

The ADC resolution is defined as the smallest incremental voltage that can be recognized and thus causes a change in the digital output. 

Resolution = Step size

NOTE:

If only LSB is present in the input sequence applied then the output voltage is defined as the step size.

V₀ = Step Size.

Calculation:

Given supply voltage is 20 V and 6 bit ADC

Output voltage when only LSB is present is Resolution itself.

\({V_0} = \frac{{20}}{{{2^6} - 1}}\)

\({V_0} = \frac{{20}}{{63}}\)

NOTE: In the ESE prelims calculator is not allowed so we will do the approximate calculation.

Calculate 20/64 we get the result as

\(\frac{{20}}{{64}} = \frac{5}{{16}} = 0.3125\)

But denominator less than assumed so, the fraction value increase.

According to options it will be 0.317 V

Converting into Decimal

(100110)₂ = ()₁₀

= 1 × 2⁵ + 0 × 2⁴ + 0 × 2³ + 1 × 2² + 1 × 2¹ + 0 × 2⁰

= 32 + 4 + 2

= (38)₁₀

Now the output voltage is

V­₀ = 0.317 × 40

= 12.68 V

But the value is < 40 so answer also < 12.68 V

According to options, the answer is 12.06 V