How much memory to read serial data

I try to read a measurment device with 256 pressure sensors with the arduino. The device normally works with the serial port of the computer. My question is how much data can be read by the Arduino? The device is connected with TR XR and it sends data of 256 sensors at once, eacht sensor is represented with two hexadecimals for example: 0B 02. It is not possible to ask for pieces of data the device only gives all data at once. Does anyone know how to bring this data into the Arduino ? When the data is read, all data will be processed into a 3*3 matrix with nine characters

Arduino only has 1KB of RAM for holding all variables and all data. If you use more RAM than that strange things start to happen.

You can use external memory devices to store the data as it is being received.

Standard I2C EEPROM memory has a write time of a few milli seconds. If your serial data is coming in too quickly that might be a problem.

However, Ramtron do serial FRAM which has no (practically) write delays and are plug in replacements for I2C EEPROMS.