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An on-board computer (OBC) is the brain of any satellite. This sophisticated piece of equipment monitors and controls each and every function of the satellite. It is generally a very expensive device, with cost amounting to hundreds of thousands of dollars. The problem we have addressed in this research is to conceive and design an economical, general-purpose and adaptable OBC, for use in general-purpose low-earth-orbit (LEO) micro-satellites. The hardware and software design of this OBC is based upon open and flexible design architecture. The idea is that the design can be used in or adapted for a variety of small LEO micro-satellites with minimal modifications. Keeping these goals in view, a complete architecture of the OBC has been developed. The design is based on the Intel 80386EX microprocessor technology. In addition, requirements for the on-board and ground station software have been identified and concrete guidelines for design and implementation of the related software have been provided.