An interface manages the exchange of information between a bus system and a memory during reading, according to a communication protocol. The interface has a protocol-decoding unit, which receives from outside commands and information for managing the reading and generates a wait-code enabling signal, and a wait-state generating unit, which is connected to the protocol-decoding unit and outputs wait codes upon receipt of the wait-code enabling signal. When the memory ends reading, as signaled by switching of a read-state signal, a wait-state disabling circuit generates and supplies an end-of-waiting control signal to the wait-state generating unit, which thus outputs an end-of-waiting code.