Question

We have an analogue to digital converter (ADC) described as 8 bit, with a 3V reference and 0V offset. What is the resolution, expressed in millivolts? Q6 (a) (b) For an input voltage of 0.6V, what is the digital output value of the ADC described in (a)? Express your answer in both binary and hexadecimal An industrial oven has a thermometer that outputs a voltage from 0 to 1V for a corresponding range of temperatures of 0 to 500°C. The thermometer is connected to the ADC described in (a). If our microcontroller needs to read the temperature to within 1°C resolution, explain why this is not possible? (c) (d) What two things must we change to remedy the problem we found in (c)?

(a) We have an analogue to digital converter (ADC) described as 8 bit, with a 3V reference and 0V offset. What is the resolution, expressed in millivolts? [2]

(b) For an input voltage of 0.6V, what is the digital output value of the ADC described in (a)? Express your answer in both binary and hexadecimal. [3]

(c) An industrial oven has a thermometer that outputs a voltage from 0 to 1V for a corresponding range of temperatures of 0 to 5000C. The thermometer is connected to the ADC described in (a). If our microcontroller needs to read the temperature to within 10C resolution, explain why this is not possible? [3]

(d) What two things must we change to remedy the problem we found in (c)? [4]

Answer 1

a) 8 bit s can represent 2⁸ = 256 values.

Therefore analog resolution = smallest possible voltage change that can be represented by the ADC

                                         = full scale voltage range/no. of levels

                                         = (3 V - 0 V)/256

                                         = 0.01171875 V

                                         $\approx$ 11.72 mV

b) 0 volt is represented by the bits 00000000 and 3 V is represented by 11111111.

    if 0.6 is represented by the n-th level, n*resolution = 0.6

    => n*3/256 = 0.6

    => n = 51.2 $\approx$ 51 (rounded-off to closest quantization level; 0.2 represents quantization error)
                      = 32 + 16 + 2+1
                      = 0⁷+0⁶+ 2⁵ + 2⁴ + 0³ + 0² + 2¹ + 2⁰

=> (0.6)₁₀ = (00110011)₂ =(33)₁₆    [ $\because$ (0011)₂ = (3)₁₀ = (3)₁₆ ]

c) 0 to 1 V is represented by 1*(3/256) = 85.33 $\approx$ 85 levels

85 levels represent (5000-0) ^oC = 5000 ^oC

=> Each level represents = 5000 ^oC/85 = 58.8235 ^oC $\approx$ 59 ^oC

i.e. the resolution of the temperature reading is 59 ^oC. Hence, it is not possible to read the temperature to within 10 ^oC resolution.

d) If the thermostat output is 0 to 3 V instead of 0 to 1V, then all 256 levels are available to represent 0 to 5000 ^oC.

=> Resolution = 19.5312 ^oC $\approx$ 20 ^oC

Even if the thermostat output range is equal to the full scale range of the ADC, temperature cannot be read at a resolution less than 20 ^oC.

However, if a 9-bit ADC is used instead of a 8-bit ADC, then 2⁹ = 512 levels are available for representing 0 to 5000 ^oC.

In this case, resolution = 5000 ^oC/512 = 9.7656 ^oC $\approx$ 10 ^oC

Therefore, the two changes required to be made to remedy the problem in c):

i) Use a 9-bit or higher ADC instead of 8-bit

ii) Use a thermostat whose output voltage range is equal to the full scale analog voltage range of the ADC