An 8-bit Analog to Digital converter (ADC) is required to convert an analog input in the range 0-5V to an accuracy of 5mV. Find the value of n.

An Analog to Digital Converter (ADC) is a device that converts continuous signals to discrete digital numbers. The performance of an ADC is primarily defined by its bandwidth and signal-to-noise ratio. The resolution of the ADC indicates the number of discrete values it can produce over the range of analog values. The resolution can be defined by the number of bits in the digital output, with each bit representing a binary value.

The resolution of an ADC is given by the formula:

Resolution = Vref / (2^n - 1)

Where:

• Vref is the reference voltage (in this case, 5V)
• n is the number of bits in the ADC (in this case, we are asked to find this value)
• 2^n - 1 is the total number of possible output values of the ADC

We are given that the accuracy required is 5mV. This means that the smallest change in voltage that we want to be able to detect is 5mV. Therefore, we can equate this to the resolution and solve for n:

5mV = 5V / (2^n - 1)

Rearranging for n gives:

n = log2((5V / 5mV) + 1)

Calculating this gives:

n = log2((5000 / 5) + 1) = log2(1001) ≈ 10

Therefore, an ADC with a resolution of 10 bits is required to achieve an accuracy of 5mV over a range of 0-5V.

Parameter	Value
Vref	5V
Accuracy	5mV
n	10

This means that the ADC needs to be a 10-bit ADC to achieve the required accuracy.