I was able to communicate with the ADC today using my code alone. I have finished deciphering the datasheet and now know how to get any information off the ADC that I need. Using my logic analyser, I was able to see the traffic that the BeagleBoard was sending out and it was a great help. The read and write functions appear to send 1 additional byte more than I thought and I never would have guessed without the analyser.
Now I move onto hooking up the IR sensors to the ADC input pins and getting some real data from the boards. The IR sensors need a 5V source, which is provided by my supply that is powering the ADC and high side of the translator. Using the figure off the the ADC datasheet, I found out that the peak output value for the sensor is when it is 15cm from something and it outputs 2.75V. I found this data from this graph off of page 5 of the ADC datasheet:
After some testing, I found that using the onboard voltage reference (which is only 2.5V) the ADC cannot distinguish the entire range it should be able to. Since the ADC compare the 2 voltages, I need to have a higher voltage than what my input it, and I chose 5V because I have it easily accessible. Now I will only use slightly more than half of the ADC range but it is a 12-bit ADC so this should be no problem.