First off, what is multiplexing? What about Charlieplexing? Any differences?
Actually, they are they same... Charlieplexing just takes multiplexing to a higher level. Both are techniques used to not only reduce the number of microcontroller pins needed, but also to reduce the power requirements substantially. However, at the cost of time and/or brightness.
In multiplexing, an entire digit or row of LEDs are shown at one time. After some time, the whole digit or row is turned off and the next digit/row is turned on, etc... Simple!
However, Charlieplexing is a bit more complicated in that it goes deeper than multiplexing. Instead of turning on a whole digit or row, a single segment or individual LED is turned on/off. After some time, the segment/LED is turned off and the next segment/individual LED is turned on, etc... After cycling through a digit/row, the process repeats with the next digit/row. So, if you're charlieplexing a 7-segment, you would consume a max of 20mA vs 160mA in multiplexing since only 1 segment is on at a time. The severe downside is that it takes longer to display information and brightness is reduced because the program needs to cycle through all the 7 segments + decimal or each LED first before moving to the next digit or row. You will also notice a slight flicker as you chain more displays/LEDs.
Look above for a comparison on multiplexing and charlieplexing. Notice how charlieplexing requires more time to display a number?
Before you tackle your multiplexing project, you must lay everything out--research as much as you can. Otherwise, you will end up wasting time, money, and pulling your hair out of frustration.