One good way to find useful things to do, it to look into mobile phone SoC architecture and try to re-implement some of the IP cores.
Simple useful things, which are likely to be part of cell libraries to be building blocks for larger parts.
Combinatoric:
- adder
- multiplier
- sqrt
- https://en.wikipedia.org/wiki/Digital_comparator
- IEEE floating point
Sequential:
- counter
- power of 2 frequency divider with counter
Real super complex projects that companies get into:
- CPU
- GPU
- video codec, e.g. MPEG
- signal processing. TODO: what exactly is implemented?
- Bitcoin mining