How much voltage does a green LED need to be supplied? Will it handle 5V?
Some logic chips have definite current limits built into their output structure, but many do not. 
Depending on the logic chips being used you may well be able to direct connect the LEDs from output to ground, but I'd suggest you should not. 

The forward voltage rating of your Green LEDs depends on the silicon elements and dopants used, but is likely somewhere from 2.2 to 3.3 V when conducting.

This might help you for the various LED colors:


What I would suggest is that you should connect your LED with a 1K Ohm resistor directly to +5V and ground. This will allow you to measure the forward voltage (even if it's not very bright) across the LED. 
From this voltage you can then calculate a series resistor to suit your application and set the LED maximum current.