Help check my (basic) understanding

retrolefty:
No. Think about a given pattern you may want to display that turns on all 16 leds of a single level (Row) going to a single output pin driving that row. That could be 16 X 20 milliamos of current which is more then the poor row enable pin can supply, hence the need to use 4 switching transistors to drive the 4 levels (Row). That make sense?

Regardless, I am amidst some heady (for me) reading on transistors and hope to understand the use of them for this project if necessary. I have some 2N2222's here and was initially planning on using these on the rows but am having some serious trouble understanding the calculations behind choosing correct resistors to use with the transistors. Any "beginner language" help would be greatly appreciated.

A 2N2222A transistor is really not able to switch 16 x 20ma of current, you need a 'bigger' transistor.

Yes, that does make sense. I was assuming (incorrectly) that multiplexing was for every LED. That is, only one LED would ever be lit at a time, not just for those in a single column (driven by a single pin).

I am starting to track with the transistors and think I am getting some of the math down...

So the max current that would potentially need to be sunk(?) from one level is 20mA*16 == 320mA
I've read that you should build in some sort of safety factor, of say 2, when selecting the transistor. In this case I would need a transistor with a collector current (Ic) of 640mA minimum.

What should I set by base current (Ib) to? I understand it can be low. Is there a rule of thumb at play here? I'll assume 20mA for the Ib?

Hfe, or the gain (amplification) to the base current, is allegedly calculated Hfe==(5Ic)/Ib where 5 is a factor used to ensure the switch closes "hard." If this is correct, Hfe=(5.64)/.02 == 160mA min. I think things are falling apart here as I am not finding transistors that seem to fit this math. If things were correct, I'd now go to the store and try to find a transistor that has a minimum Hfe of 160mA, with a minimum Ic of 640mA, operating at 5V (or should this be 5V - LED voltage drop?).

When trying to "shop" online for a transistor that fits the above specs I was not finding much. I believe I am doing something horribly wrong here.