Circuit Diagrams available on the net as scan
of hand-drawn circuit.
BBC Documentation
Project Technical Information and software
8-bit software
More BBC stuff.
The BBC micro is more complex than the Atom, but much of it could be cloned. If you just need something that can play games on your TV, then the main jobs are the 6845 CRTC and the Video ULA. There is public source for a VHDL 6845, though it lacks some features like vertical total adjust that may be required for smooth scrolling on the BBC micro.
Video
The Video ULA contains mainly shift registers and a 4-bit to 4-bit palette.
The 6522 VIA provides the keyboard interface.
Sound (optional)
The SN76489 chip provided sound. It is no longer available. This has been implemented in VHDL by Arnim Läuger, for his Colecovision project.
Joysticks (optional)
The NEC7002 ADC chip allows joystick control. Also obsolete and will need cloning
Both are obsolete. Alternatively you could get your PC to write suitable values into some dual-ported registers, getting round many I/O obstacles.