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The 6502 is one of the most heavily preserved technologies: http://www.visual6502.org/JSSim/index.html

Full die capture, full transistor level simulation.

Most of the others are being emulated in proportion to their importance to games, in arcade machines and consoles. Those emulations are going to be as cycle-accurate as required.

There are some issues around things like the Yamaha synth chips, which are mixed-signal and depend on analogue properties that can be difficult to emulate.

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A lot of effort goes into accurately emulating historic processors in the MAME project, as well as other vintage hardware. It's generally accurate enough that MAME is regularly used to emulate vintage hardware when reverse-engineering devices.
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Quite a few. There's a great project to do cycle accurate emulation of the 8086, too, which is more my area of interest than 6502.

Note that 6502s are still being produced, albeit in a modern CMOS version.

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Most fun I ever had with a 6502 was when I realized that, at 1 MHz, I could do 250,000 average instructions per second. So I divided my monitor up into 20 boxes to have 12500 (fairly complex!) instructions per per second for each box. I used them to separately animate the contents of each box differently.

Just calculating or shuffling data around was invisible. With that visualization I first realized how much stuff could be done with a 1MHz CPU.

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