Ah, memories of one of my very first lab assignments in digital circuits engineering class (back when computer science was still busy splitting off from applied mathematics and electrical engineering). We were given nothing but a breadboard, some chips with basic logic gates (NANDs, multiplexers/demultiplexers), an EPROM, access to an EPROM burner (w/ hex keypad!), some LEDs, switches, resistors, jumper wires and a power source.

The assignment was to build a traffic light simulator, set the whole thing running, change the traffic lights as a result of switch inputs acting as sensors and a simulated interval timer.

Some students were baffled by this (lectures hadn't caught up with lab assignments at that point): how could you build a small processor using only logic and an EPROM? There's no memory or registers to keep state!

This is what differentiates combinatorial logic from sequential logic: feedback. Use some of the EPROM's data outputs along with logic gates and switch outputs (using the multiplexers / demultplexers) as address inputs to the same EPROM.

Sweet memories of solving Karnaugh maps, Quine-McCluskey minimization, logic hazard mitigation, etc. Good times.