The machine uses the "canonical" encoding, but with the second output digit shifted by +1 modulo 6 (so that, e.g, Gold = 5 in the first digit and 0 in the second digit).

The algorithm is very naive, simply converting each digit of the binary string into its senary equivalent and adding them together. The units are encoded on the sixfold rotational symmetry of a 2-atom molecule; the carry is stored as quicksilver and used to project the sixths place digit. Addition goes from most to least significant digit, so that the parity of the molecule is always 0, 2 or 4 until the final input bit is processed. This means that, for example, the bonder next to Arm 7 is always safe to swing over. It costs 1 cycle per tape loop to rotate the molecule back into the "correct" orientation--the encoding shift is therefore a natural consequence of the machine geometry.

Inputs starting 011 and 101 both require carry, but these two states cannot be collapsed into one another. A funky side effect of the way this is handled is that the two atoms of the molecule swap places in the 011 case.