The transition function can only do modular addition within a cell, but the paper also describes how to build a k-ary counter. If your single state has the inc

The transition function can only do modular addition within a cell, but the paper also describes how to build a k-ary counter. If your single state has the increment lookup table for a single cell, you just need to move to the next cell to do carries, and move to the previous cell to leave the counter when you're done. A special carry character is written instead of zero to make sure you leave the whole counter, and you convert it to zeroes as you leave.