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Re: what does the term "trace" in an emulator mean
If you're talking about EPROM emulator, then trace it's a powerfull emulator's feature to record each address touched by the device which access the EPROM (most of the time a microcontroller).
Thus you can watch every step done by microcontroller running the program from external EPROM and take a note if for example gets stuck in an endless loop.
If you're talking about trace in microcontroller emulator, then it's very similar with above. The trace buffer is a high speed RAM used to capture in real time all the microcontroller events on bus and pins.
When capturing the trace may be filtered before the information is stored with the use of complex events and after the acquisition by choosing the filter menu.
You can even stop tracing after a specified number of frames have been captured. All this nice features are strong related to specific emulator.
To add to Silvios excellent reply;
While debugging you might end up "in the woods" you have no idea how you got there. If you have a trace function, you can look backwards, where did I come from. In general, JTAG debuggers do not offer trace but breakpoints only. With breakpoints, you execute a program until you get to the location you defined as break point. The execution stops and you can examine memory contents, register contents and so on. What you can not do is looking backwards.
Trace is something like the rearview mirror including a recorder.
Hope I did not confuse you too much