Recently I have constructed two small LED matrix scrolling message tag. A 16F57 controller was used. The program was written in XC8. Almost all of the program FLASH is used (nearly 90%).
Since this is for demonstration only, I made the source code available: http://pic.hitechworld.org/data/ledmatrixtag/
One board has 10 columns and 5 rows, the other has 2 additional columns (12 columns, 5 rows). It is sufficient to scroll through text messages. A serial RAM chip is used as bitmap buffer for the complete scrolling text. These chips have 8K capacity. Typically, scrolling text bitmaps will require 60 to 100 bytes only. Long texts of course may require more. But it is still less than 256 bytes. The 16F57 however only has small internal RAM, of which most is used up. It is also partitioned into 16 byte chunks.
No resistors are used at all. The matrix boards can work from 4.5 volts although normally 3 volts are used. 4.5V is the maximum voltage for the serial RAM ICs! The boards also have a CR2032 battery holder. Clocking is done using 330uH inductors.