Turing Tumble Community

Square the register

The object of this challenge is to given a 4 (gear) bit register, square this number every time a blue ball is released. Register A must start at 5 or less.
You will have more than 8 gear bits and will need more room than the original Turing Tumble board.
Here is the starting position:

ttsim (2)

Click to open the sim.
You may need to upload image.
Also, the sim is not for mobile.
I am looking for a solution.