In recent years, many applications have been implemented in embedded systems and mobile Internet of Things (IoT) devices that typically have constrained resources, smaller power budget, and exhibit "smartness" or intelligence. To implement computation-intensive and resource-hungry Convolutional Neural Network (CNN) in this class of devices, many research groups have developed specialized parallel accelerators using Graphical Processing Units (GPU), Field-Programmable Gate Arrays (FPGA), or Application-Specific Integrated Circuits (ASIC). An alternative computing paradigm called Stochastic Computing (SC) can implement CNN with low hardware footprint and power consumption. To enable building more efficient SC CNN, this work incorporates the CNN basic functions in SC that exploit correlation, share Random Number Generators (RNG), and is more robust to rounding error. Experimental results show our proposed solution provides significant savings in hardware footprint and increased accuracy for the SC CNN basic functions circuits compared to previous work.