Mod 7 in Manufactoria
The algorithm is quite straightforward: Compute the modulus using a state machine (the largest part with eight branches - one of the states is duplicated for logistical purposes), then encode and collect the results. Since almost every result contains a one digit, an extra compression step is employed to reduce the amount of parts.

Designed in yEd, then transcribed to Manufactoria. 

Uses way too many conveyer belts, in my opinion.