Increasing applications of fundamental biological gates have been successfully built during this decade. Proceeding to the current development, this study presents a genetic arithmetic and logical unit (ALU) design based on a series of genetic logic gates. The system level's architecture consists of three parts: temp register, ALU and accumulator register. Using the concept of the ALU on the digital computer, the authors present the fundamental function of the genetic ALU via full adder register and also build the bio-storage devices to store data generated from the genetic ALU. The system in this study shows the capability of computing and storage on the biocomputer.