Nice idea. I like it.
Tubes et all.
My general understanding is that in early computing, pre-solid state technology, a bit would represented by a single vacuum tube.
That would be a missconception to start with. A tube doesn't store anything. In 'tube based' computers, tubes (usually triodes) provide a
NOT functionality, as
OR are made up of resistors and diodes.
But there where some specialized storage tubes, but different from what you imagine. One was the Williams tube, basicly a CRT where dots could be read back. The other was the Selectron tube. also using the same effects, but with a more sohisticated and adapted design. Both vanished soon for core memory.
Havin said that, regular tubes where of course used also to store bits - as part of a Flipflop - but it always (*1) needs two triodes. The first (documented) one would be the Eccles–Jordan trigger circuit (patent filed 1918).
Since double triodes - two triodes in one glas tube - are usually used, the impression may arise that only one tube is needed.
A tube based flipflop may look like this:
The Display (Background)
I could imagine putting together some LEDs, some cheap switches, and an Arduino or a Raspberry Pi to make such a device.
But, ideally, I'd like to use vintage parts, so that this device could not simply illustrate binary, but also provide at least a glimpse of the ways that binary data has been physically represented.
Yes, that's the real way :))
Is there a feasible way to build a byte using vacuum tubes, whose value could be changed with electrical switches,
Yes, it is, and it isn't a lot of work.
and then have some sort of interface to connect it to a Pi (or something else) to read its value and output it to a screen?
Naa, that'll kill the whole effort. I'd strongly suggest to keep complete free of modern computing/controlling parts. Otherwise the pupils may come up with the idea that it's faked anyway. No hidden (or visible) modern devices should be harmed when making this demonstrator :))
I could also use something that isn't a vacuum tube (I could use individual transistors for instance). I like the idea of vacuum tubes chiefly because it can help illustrate a longer history of computing technologies.
As Manassehkatz already pointed out, relays do make a great demonstrator. Here the students can see the bits physically switch. It's even possible to add mechanical markers to display the state of each bit - providing a way to read the data without any electronic support :))
The Display (Suggestion)
Go with a set of relays displaying your data - maybe 4 for a number, or 8 for a byte - configured as a latch holding the last input. To set new data have 4 (or 8) flip switches where any new data can be configured, and a button enabling these setting so be transferred into the latch.
This setup shows that the storage is real and not just the direct result of the switches (like light and lightswitch at home). Data can be changed as often as needed until it's transferred, and stored data won't change until a new transfer is initiated (button pressed).
LEDs can be used in conjunction with the relays and the switches to show each state independently and continuously.
As an addition (or alternative) a decimal input could be constructed (at least for the 4 bit/numeric version). Have 10 buttons (0..9) and a diode matrix to encode them as BCD. Here each switch would trigger the latch right away. Showing much functionality with next to no parts(*2).
In fact, with the numeric version you could use the saved 4 relays to store a second number - like whenever a new input gets stored in the first 4 relays, their content gets transferred to the second first - thus showing even data transfer between latches - and a simple input routine - in pure clear, clicking and moving hardware.
With sufficient contacts on your relays it would be rather easy to extend this with an adder function summing up both digits and displaying the result...
... I'm not getting carried away on that, am I?
Long story short, relays are an extremely handy tool to explain the basics. And you'll be surprised how versatile a large enough bunch of switches is :))
Oh, and one more thing: Relays allow you to build all of this using low voltage, like all 5V (or even below), so no danger as with tubes and neon lamps. Not to mention the way simpler power supply to be used (*3).
*1 - There are designs that can keep a bit with just one tube, but not for generic use
*2 - And no bloaty Java libraries just to convert some input :))
*3 - With a small enough setup a standard USB wall-wart might be enough to supply the device.