Stochastic computing (SC) is a re-emerging approach adopted in vision and learning machines. SC, as a hardware-efficient unconventional computation paradigm, utilizes digital logic systems for arithmetic operations. Conventional logic gates are fed binary streams that hold corresponding pulse probabilities. The similarity between binary input pulses is crucial to the correlation. In this brief, the utilization of a contingency table (CT) in an SC simulation is proposed as a main contribution. The CT manipulates input scalars to perform SC-based logic operations, which avoids lengthy bit-by-bit bitstream processing. After positive and negative correlation tuning via CT, three different approaches to emulate uncorrelated bitstreams are studied. Taking advantage of the ease of a memory- and runtime-efficient CT, correlation occurrence and error analyses are thoroughly discussed. The ability to use a CT for all input combinations instead of bitwise processing in any simulation environment is ascertained.