Computation performed on stochastic bit streams is less efficient than that based on a binary radix because of its long latency. However, for certain complex arithmetic operations, computation on stochastic bit streams can consume less energy and tolerate more soft errors. In addition, the latency issue could be solved by using a faster clock frequency or in combination with a parallel processing approach. To take advantage of this computing technique, previous work proposed a combinational logic-based reconfigurable architecture to perform complex arithmetic operations on stochastic streams of bits. In this paper, we enhance and extend this reconfigurable architecture using sequential logic. Compared to the previous approach, the proposed reconfigurable architecture takes less hardware area and consumes less energy, while achieving the same performance in terms of processing time and fault-tolerance.