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You could also go ahead and just loop through every single byte writing every possible value and reading it back to see that it stores each value.
Which won't necessarily tell you if writing one byte isn't annihilating some other byte (though I don't know how common this might be with these types of RAM). Something like what memtest86 does, writing random data and then checking it again (several passes), might be a better bet. An
LFSR would seem to be a good psuedo-random generator to try, as mentioned
here.