The screenshot provided is the basis of the everything calculator. This algorithm takes advantage of a simple fact about numbers. Numbers can be expressed as recursive multiplication and addition.
27182 = ((((2*10) + 7)*10 + 1)*10 + 8)*10 + 2

How this device works is a supply of tens is fed from the bottom pipes. The side inputs are the digits. From the top down, the first one is the ones place. Second one is the tens place. Third is hundredths. etc.

Expanding on the basic prototype. Add around 20 operators per layer to ensure maximum output.
Create a 10s factory that will supply 10s from the bottom pipe.
Create a 0-9 digits warehouse near the right inputs of the machine.
This wiring gives 18145.

So, the next time you need a new number, simply erase the wiring within the rectangle area meant for wiring the digits. Once you wired the digits, you can then copy and paste the wiring to your other machines.

Here is the machine with empty wiring.

Here are multiple machines in compartments.