A series of rotary switches provides a rather convenient data input of addends.
This is an old eBay find and it's very handy !
I've torn one apart to show the internal wiring, and it's a pretty simple binary encoder :-)
I've used some of these for the (semi-aborted) attempt at a front panel for the #Quick & Dirty Frequency Generator
For this project, though, there will be no mode push-buttons or bypass '595. TIL311 are perfect for the desired futuro-vintage look and feel of hexadecimality.
I'll keep the "one lamp in series with each coil" idea but it's good to visualise the hexadecimal value. I might create "slices" of 4 or 8 bits on the perforated proto board (I'll use bakelite for extra "oldtimer" feel).