Modern deep learning schemes have shown human-level performance in the area of medical science. However, the implementation of deep learning algorithms on dedicated hardware remains a challenging task because modern algorithms and neuronal activation functions are generally not hardware-friendly and require a lot of resources. Recently, researchers have come up with some hardware-friendly activation functions that can yield high throughput and high accuracy at the same time. In this context, we propose a hardware-based neural network that can predict the presence of cancer in humans with 98.23% accuracy. This is done by making use of cost-efficient, highly accurate activation functions, Sqish and LogSQNL. Due to its inherently parallel components, the system can classify a given sample in just one clock cycle, i.e., 15.75 nanoseconds. Though this system is dedicated to cancer diagnosis, it can predict the presence of many other diseases such as those of the heart. This is because the system is reconfigurable and can be programmed to classify any sample into one of two classes. The proposed hardware system requires about 983 slice registers, 2,655 slice look-up tables, and only 1.1 kilobits of on-chip memory. The system can predict about 63.5 million cancer samples in a second and can perform about 20 giga-operations per second. The proposed system is about 5-16 times cheaper and at least four times speedier than other dedicated hardware systems using neural networks for classification tasks