How to build logic gates?
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.







simulate this circuit &ndash; Schematic created using CircuitLab

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.