Most digital systems operate on a positional representation of data, such as binary radix. An alternative is to operate on random bit streams where the signal value is encoded by the probability of obtaining a one versus a zero. This representation is much less compact than binary radix. However, complex operations can be performed with very simple logic. Furthermore, since the representation is uniform, with all bits weighted equally, it is highly tolerant of soft errors (i.e., bit flips). Both combinational and sequential constructs have been proposed for operating on stochastic bit streams. Prior work has shown that combinational logic can implement multiplication and scaled addition effectively; linear finitestate machines (FSMs) can implement complex functions such as exponentiation and tanh effectively. Building on these prior results, this paper presents case studies of useful circuit constructs implement with the paradigm of logical computation on stochastic bit streams. Specifically, it describes finite state machine implementations of functions such as edge detection and median filter-based noise reduction.