A lot of the ZX Spectrum functionality and logic is in the ULA, an ASIC.
There's a whole book on the ULA - http://www.zxdesign.info/book/theZXSpectrumULA.shtml
Actually there is now design out of 74ls series logic that replicates functionality of the ULA (it is probably completely bug-for-bug compatible), IIRC it was designed by author of said book.
Nice, I'm thinking about making it possible to connect it directly to a display/TV and keyboard. Now, I have to have a terminal or laptop + terminal emulator.
It seems hard to drive a vga display without resorting to fpgas or an avr.
If composite is enough, the NES PPU could be a fun addition to that design :)
Apparently, it can be done with a bunch of TTL logic chips.
Yes, the composite solutions sounds more fun :-)
https://www.youtube.com/watch?v=8rWCYo1UcOQ