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An input and output device is a device that accepts data from the user is input, processes it and displays the output.
Fax machine accepts input from the user by scanning documents, accepting audio from the microphone and the output is given to the user as audio from the ear piece and printing documents.
A modem is a device that converts binary signal to digital signal. It accepts the input as the data coming from the service provider as binary and translates it to digital and provides the output to the computer or the router as hexadecimal or decimal data.