# Analog to Digital Conversion

Note

The LabVIEW run-time engine needs to be installed on the computer (Windows only), and can be obtained for free from here (user registration required, also free):  http://www.ni.com/download/labview-run-time-engine-2010-sp1/2292/en/

Simulations themselves can be obtained here:  https://sites.google.com/a/cord.edu/labview-for-analytical-chemistry/

1. Calculate the total number of possible values that the digital value can take for each of the following bit depths: 2-bit, 4-bit, 6-bit, 8-bit, 10-bit, 12-bit, 14-bit.  For example, with 1 bit of resolution, there are 21 = 2 possible binary values.
 Bit depth Values 1 2 4 6 8 10 12 14 2
1. For each of the bit depths in question #1, determine the minimum value and maximum value for each bit depth. For example, with a bit depth of 1 bit, the possible values are 0 and 1, so the minimum value is 0, and the maximum value is 1.
 Bit depth Min. Max. 1 2 4 6 8 10 12 14 0 0 0 0 0 0 0 0 1
1. Start with an Amplitude of 1.00 V, a resolution of 4 bits, and a range of ±10 V and have the simulation run continuously. As you increase the amplitude, describe how the analog and the digital signals change.

1. What is the difference between an analog signal and a digital signal?

1. Explain what happens in analog-to-digital conversion in such a way that a technologically illiterate grandfather could understand it.

1. Assuming that you are digitizing an analog voltage between 0 and 5 volts, calculate the difference in voltage that corresponds to an increase in the raw count by 1 for each bit depth. Looking back at the number of values for each bit depth will be helpful.
 Bit depth Voltage difference 1 2 4 6 8 10 12 14
1. Reset to an Amplitude of 1.00 V, a resolution of 4 bits, and a range of ±10 V. How does the correspondence between the analog and digital signals change as you decrease the range?  What is the significance of the Step Height?

1. Reset to an Amplitude of 1.00 V, a resolution of 4 bits, and a range of ±10 V. How does the correspondence between the analog and digital signals increase the resolution (also known as increasing the bit depth)?  Why does the step height change?

1. Using an A/D converter with 12-bit resolution and an input range of ±10 V, at what analog signal amplitude do you begin to see distortion of the analog signal due to digitization?

1. How does your answer change if you switch to 16-bit resolution and an input range of ±10 V?

1. How does your answer change if you use 12-bit resolution but with an input range of ±1.25 V?

1. Why does a higher resolution give a better digital representation of small analog signals?

1. Why does a smaller input range give a better digital representation of small analog signals?

1. If your signal also had noise present (and assuming that the amplitude of the noise is small compared to that of the signal), would you choose a smaller or larger input range to avoid recording it along with your signal? Would you choose a lower or higher resolution (bit depth) to avoid recording it along with your signal?  What Analog-to-Digital Conversion issues arise as the amplitude of the signal gets smaller (while the noise amplitude remains the same)?