Understanding ADC Resolution Calculation

This question asks us to find the resolution of an Analog to Digital Converter (ADC). The ADC has a specific input voltage range and a certain number of bits for its digital output.

Key Information Provided:

• Input Voltage Range: -5V to +5V
• Number of Bits (Coding): 8 Bits

What is ADC Resolution?

The resolution of an ADC tells us the smallest change in the analog input voltage that the converter can detect or represent. It's essentially the size of the smallest voltage step the ADC can distinguish.

Calculating the ADC Resolution

We can calculate the resolution using the following formula:

Resolution = (Total Voltage Range) / (Total Number of Possible Output Codes)

Let's break down the calculation step-by-step:

Step 1: Determine the Total Voltage Range

The input range spans from -5V to +5V. To find the total range, we subtract the minimum voltage from the maximum voltage:

Total Voltage Range = (Maximum Voltage) - (Minimum Voltage)

Total Voltage Range = $(+5 \text{V}) - (-5 \text{V})$

Total Voltage Range = $5 \text{V} + 5 \text{V} = 10 \text{V}$

Step 2: Calculate the Total Number of Output Codes

The number of bits determines how many unique digital codes the ADC can produce. For an N-bit ADC, the total number of codes is $2^N$.

In this case, N = 8 bits:

Total Number of Codes = $2^8$

Total Number of Codes = $256$

Step 3: Calculate the Resolution in Volts

Now, we plug the values from Step 1 and Step 2 into the resolution formula:

Resolution = $\frac{10 \text{V}}{256}$

Resolution $\approx 0.0390625 \text{ V}$

Step 4: Convert Resolution to Millivolts (mV)

The options are given in millivolts (mV), so let's convert our calculated resolution:

Since $1 \text{ V} = 1000 \text{ mV}$,

Resolution = $0.0390625 \times 1000 \text{ mV}$

Resolution $\approx 39.0625 \text{ mV}$

Comparing with Options

The calculated resolution is approximately $39.0625 \text{ mV}$. Comparing this to the given options:

• 3.9 V
• 0.39 V
• 3.9 mV
• 39 mV

The value $39.0625 \text{ mV}$ is closest to 39 mV. Therefore, the resolution of the ADC is 39 mV.