I completed construction of my first model, have tested it, and it works as it should. Here is how it looks complete:

And here is schematics:

Having accomplished this first goal of making proof of concept, I am going to take the next step - making model system consisting of four 1-bit registers on the same bus. But now it will not only be mere scaling up of above model, but the registers should be addressable, the model should have controls for choosing the source and destination registers and for setting them up properly.