This paper describes on a position detection method for the motors which have repetitive operations using the Algorithmic State Machine(ASM), one of the digital logic design methods. With analyses for the incremental encoder output patterns, state diagram and state table are constructed and a digital circuit which can detect the changing point of direction of motor rotation is designed. To verify the validity of the designed circuit, simulations for all cases in which the direction of motor rotation is changed, are performed. Simulation results show the designed digital circuit can detect the direction of motor rotation accurately for all cases.