Convolutional Neural Network (CNN) is widely acknowledged as an effective machine learning model for various detection and recognition tasks. However, CNN often requires a significant amount of hardware resources and is high in its power consumption. This hinders the widespread deployment of CNN model in embedded systems and wearable devices. Therefore, stochastic computing (SC) which leverages the power-accuracy trade-off, began to gain popularity in various neural network (NN) implementations. This paper presents an improved SC multiply-and-accumulate (MAC) unit that can be utilized as convolution engines in CNN. The proposed SC-MAC is operated using deterministic sequence and the design achieves latency and power reductions through parallelism and split mechanism optimizations. Furthermore, we also introduce decoder-based Stochastic Number Generator (SNG) that is capable of generating uncorrelated and segmented stochastic number (SN) without using random sources. The proposed deterministic and split SC-MAC is synthesized using typical libraries of UMC 40 nm technology for detailed hardware evaluation. The functionality of the presented SC-MAC is also verified in CNN using the MNIST dataset. Overall, our SC-MAC is proven to achieve higher power efficiency (GMACS/mW) and lower in energy consumption (pJ/MAC) as compared to the related works.