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Programmable memory built-in self-tests (BIST) have increased test flexibility but result in large area overhead. In this research, a new finite state machine (FSM) based programmable memory BIST that can select march algorithms was proposed in order to overcome this problem. The proposed BIST efficiently generates various march algorithms utilizing an extended address counter while also taking into consideration the characteristics of the march algorithms. The experimental results of this research indicated that the proposed BIST improved test flexibility and resulted in a smaller area overhead, as compared to the results of previous studies.