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I think an Arduino Scope is a really nice idea and I have been looking for one all over and most are pretty bad. Girino, even though now over 5 if not 7 years old, it is still the best project around as far as I know. It's best because it pushed the limit to frequency of data acquisition you can do on an Arduino.
I have spent a few days with this and had mixed results. To make a long story short: if your want a scope for helping you test your TTL breadboard circuits, then you can use the Girino source code on a NANO, stuck in the breadboard. You won't need any of the op-amp circuits which I found didn't work well at all. All you need to do is (1) hook up +5 V and (2) GND to power and ground bus respectively, (3) connect pin A0 to D6 before you plug the NANO into the breadboard, that copies the signal input A1 to the trigger comparator + input AIN0 on D6; (4) a 1 kOhm resistor from D3 (PWM out) to D7 (trigger comparator - input AIN1), and a 1 uF capacitor from D7 to the GND bus. Finally your signal input goes into A1 (or D6 because of the bridge) and that's it!
This is super simple and perfect for observing your TTL signal switch, for example, when building edge detectors with capacitors.
I found the op-amp stuff didn't work well at all as it lead to losses, i.e., instead of 5 V I ended up with 3.7 V on the signal input), and the switching between the 2.5 V offset and no offset isn't right as it leads to a 0.6 V offset even if you don't want an offset. Supposedly the op-amps should "decouple" and protect your input pins, but if your signal input in in that 5 V range then there is no point in doing that. If your input is very low as in analog amplifier circuits, then you'd need to have real amplifying op amp circuits. You could do that since the basic setup with the NANO is so simple and leaves the entire rest of the breadboard free to experiment.
The project is written for the UNO but I had no UNO on hand, and the NANO, while squeezed on memory, still has 55% dynamic memory free, so I guess the data buffer could even be increased a little on the NANO. I first started with the MEGA hoping to quadruple the data buffer, but the MEGA is really dumb as it doesn't connect the AIN1 to any pin. That is a totally retarded decision as it would have cost nothing to lead the AIN1 signal that's on the chip to a pin! Heck! There's even an unused pin on the board. Really retarded. First I built my own external comparator with an LM393 and that worked, but once I discovered that the NANO can do it all, I ripped out all the external circuitry and it works like a charm for what I want it.
Now the real improvement that could be done is in the code, both the Girino "Sketch" and the Girinoscope Java code. I am looking into adding another one or more channels, because I found that I don't need a high horizontal resolution for doing some simple logic analyzing, I should be able to multiplex 2 or 3 channels into a data buffer slightly larger (maxing out the spare memory that even the NANO has).