With the increase of technological developments, the speed limit of the processors that have emerged has accelerated the reduction of nanotechnological solutions of transistors into atomic dimensions from nanometers. Physical systems in which stochastic computation is critical instead of deterministic computation by taking action from atomic behavior are discussed. For this reason, as an interdisciplinary study, this paper will discuss the application of the arithmetic-logic unit in stochastic behavior for the design issues and image processing applications. The logic level design made by considering the design constraints will be used during known image filtering operations. Probabilistic pixel values in binary that sent to the input of the arithmetic logic unit will be used in the Sobel image processing operator. The images are processed with both conventional filter and stochastic filter, then the results obtained will be given visually.