The emergence of synthetic biological circuits opens up a wide range of possibilities for maneuvering and controlling cellular behavior for many applications, including therapeutics in humans. These applications require remarkable reproducibility, and the logic circuit must demonstrate resilience against various perturbations. In this paper, we design the fundamental logic gates using a biomolecular perceptron based on the Molecular Exchange Mechanism (MEM) as its core module and extend the design to produce a winner-take-all (WTA) network implementation. The efficacy of the designs consider synthetic Boolean data and pattern classification tasks such as the MNIST handwritten digits dataset. Interestingly, the designs demonstrate improved reproducibility in comparison to other design choices, suggesting the MEM-perceptron as a potential choice for biomolecular logic implementation and pattern recognition in a molecular environment.