I'm thinking of ideas for a school project and one of the better ones was to build a calculator from scratch using only wire and basic electrical components. I've seen very many marble, Lego, domino, etc calculators that involve AND, OR, NOT, etc logic gates, but I wanted to make one purely electrically. I've seen some say that this is a very difficult project, but I have a couple months and I'm intermediately experienced in electrical engineering and have 6 or 7 EE projects under my belt. My problem is that I can't find diagrams anywhere for basic logic gates, only transistors, which feels like cheating. Any and all help is appreciated. Thank you!
Build a serial-adder. That can become a multiplier. Or a subtractor. Given a subtractor, you can build a divider.
Here is a discrete resistor-transistor logic NOR, such as used in the Lunar Lander Radar; that used ONLY this circuit, even for latches.
Note this will be rather slow, about 5MHz clock rate, maybe. For each 1-bit serial-add. For 32-bit add, you need about 6 microSeconds (160,000 per second). For 32-bit multiply (that will produce 64-bit lossless result) you need 64 * 6 = over 3,000 microSeconds, or about 300 multiplies per second.
But who is in a hurry?
If you want to build this, at 3mA per logic NOR, assuming each latch is at least 4 NOR, and 500 bit storage, you need 4 * 500 = 2,000 NOR gates at 3mA each. Thus at least 6 amperes of 3.3 volt power. Just for the latches.
Internally, logic gates are made of transistors, diodes, and resistors. This is true for all logic families, both bipolar and CMOS. Of course, the components vary among the families; that is why they have different operating characteristics. Most basic gate (AND, OR, etc.) datasheets have an internal schematic of one gate so you can see how it works. Growing gates from discrete components following these schematics isn't cheating; in some courses it is required lab work.
Be warned, it takes a LOT of gates to make a simple 4-function calculator, and that's just for the calculation part. Growing the display system from scratch is even more work.
The idea of using a 3-input NOR gate as the basis for your logic is a good one. However, I personally have a nearly-full reel of NMOS transistors, so instead of using @analogsystemsrf's RTL gate, I would go with an NMOS gate:
As far as physical construction goes, I've been toying with the idea of having a small PCB made that incorporates two such gates in a 10-pin SIP package. (See these UNI-SIP breadboards for an example of this.)
Note that it takes six 3-input gates to build a full master-slave D flip-flop, which would be three such modules.
These SIPs would plug into a wire-wrap breadboard, which would then hold the application-specific wiring. A large panel (of the type shown below) could hold a couple hundred such modules, which would be enough for a general-purpose CPU (e.g., PDP-8 or 8008).