I have made a machine that can read/write numbers.
tinyurl.com/4bqelwlb
To use it, you first make sure all gear bits are set at 0. After that, to write a number, you let x balls out of the hopper on the right, one at a time, up to 15. Then, you release a SINGLE ball out of the hopper on the left , and it will read to you what your number is! The interceptors on the bottom read, from left to right, 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14, and 15. I think I will be able to make it more compact and therefore have more bits.