How much current can a microcontroller/DSP pin sink/source?
If you google TMS320F2812, the 2nd link is to a PDF file tms320f2812.pdf; if you look in this document at table 6.2, "Recommended Operating Conditions", you can find the numbers you need. 

If you plan to connect the LED from the pin to ground (through a resistor, of course), so that a '1' output lights the LED, the number you want is Ioh, high-level output source current. Whereas if you plan to connect the LED instead to your +V supply, so '0' lights the LED, check Iol, low-level output sink current.

Looking at the numbers, you can see values from 4mA to 8mA, but you should also take note that these are in the 'MAX' column, which means these are values you should not exceed. Now, 4mA is not very much current, typical current to light an LED can be 10 or 20mA, to establish useful brightness. Were it me, I would employ some kind of driver between the '2812 and the LEDs, and try to keep the current in/out of the '2812 I/O pins well under 2mA.