Sorry, but I am not following... If I remove A16, how would they communicate? I think I need to be assessing their capability to exchange data and I'm not sure how that'd occur if one of them is removed.
Checking the exchange is the next step. First you need to check that everyone is trying to say something to the other. The fact that there is no other is not a problem.
The A16 board works for you and stops on the exchange with A2.
So the problem is A2. She needs to be dealt with. A16 can be put aside. You can leave

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Thank you, MegaVolt, but your quoted post makes no mention of where and how you measure those waveforms. Where did you connect your scope/LA (by far the biggest question here), and what were the measurement settings? Trigger (y/n, if y on which channel?), ground, etc. I can't tell what I'm looking at without that context.
So I went back to the SM and spent some additional time with 4-28 and 4-29 from p. 4-31 and 4-32. I am not sure how this is possible, but I am not seeing any "pulses" or "logic activity" on P80-2, 20, 24 and 25, regardless of the troubleshooting switches (or instrument collecting data) settings.
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You are interested in pin 25 of the UART chip (A2 U5). This is the data output to the A16 board.
Data can be transferred once when the power is turned on. You need to put one probe of the analyzer on a 5V supply and set it to trigger once when this signal appears. And put the second on 25 pin. And connect the ground. then, when the power is turned on, the analyzer will write data among which it will be possible to find one byte that was transmitted.
If it is not there, something is possible with the A2 board. You need to be busy troubleshooting on it.
1. Check the reset.
2. Check clock.
3. View other signals on the processor - WR, RD, MREQ, IOREQ, M1, A0...A15, D0...D7
4. Check the content of the memory chips
5. And then look for a microcircuit that does not do what it is supposed to.
You can record signals with the analyzer in different places of the circuit, and I will say if they are similar to what they should be. The recording conditions are the same as above for UART. 7 signals can be recorded at one time.
This can be a long-term activity. Perhaps it makes sense to open a separate topic for this. I think there are a lot of people here who can customize the Z80
