Requirement for more ADC inputs than micrcontroller has available
To read a pot, you don't need an ADC. All you need is a capacitor and a timer. Here's one way you might do it:



Begin with the input low. Leave it this way for several RC time constants so all the capacitors discharge. Now bring the input high and start a timer. Configure your microcontroller to interrupt on input change. As each capacitior charges and crosses the high threshold of your inputs, you get an interrupt. Read the timer. The number corresponds to how long the capacitor takes to charge, which is a function of the RC time constant of R1*C1, and since you know C1, you can calculate R1. When all the inputs have changed, bring the input low. Repeat.

There are hundreds of variations on this. You might put a buffer at the input if your microcontroller can't source enough current to charge all the capacitiors. You might time charging and discharging the capacitiors to double your sample rate. There are many other ways you might connect the capacitiors.