I am trying to design a counter that will count up to 9.9. In the attached files I was trying to use a 2 digit 7-segment LED, but I resorted to trying to get one digit to work first. That is why the circuit is separated. I am not able to get the LEDs to light up at all. I've tried all the suggestions on these forums to the best of my abilities but was still unsuccessful.
As this sounds like a homework problem, it would be unethical for me to just give you the answers, so.........
The first thing to do is to replace the analog grounds with digital grounds. I believe it's a quirk with MS when using digital components.
Another MS quirk; check your current limiting resistors on the display. Assume ~2V drop across the LED and calculate what the current will be when the LED is on. Right click the LED display and check the "On Current" value. I would leave it as it is since that is a good real world value and set the current limiting resistors (you don't really need the one on the common anode pin) to get a value greater then the turn-on value. In real life, the LED would have lit but would be very dim with your original circuit (as well as not having a digital vs. analog ground issue). Tie the lamp test pin (LT) on the 74LS47 to digital ground to force the LED on for debugging. Put it back to VCC when you get it working.
Now, look at the logic for your hard-wired decimal point. Does that make sense?
Check the wiring on your 555 timer. That is not right for an asyncronous counter. Also, check the values of the components to slow it down so you can see the digits change.
Also, I'm not sure if you are required to use the 74LS90 but there are other counters that are much easier to use when cascading multiple digits. Look into the 74LS160 for example.