In the AT24C16A the 16K number (16384) is the total number of bits. Divided by 8 that yields 2048 bytes. Addressing for 2048 bytes takes 11 address bits. For this part you put the three most significant bits into the device address byte as P2, P1 and P0. The next byte in the I2C communication sequence contains the lower 8 bits of the 11 bit address.

The datasheet at:
http://www.atmel.com/dyn/resou...oc0976.pdf
...tries to explain all this for the parts in this family. Do not feel bad if you were confused as many others have also been confused as well regardong the addressing scheme. I have also heard of many designers that got confused and thought that a "16K" device had 16K bytes of storage.

Several times I have attempted to make the embedded software capable of being easily configurable be able to handle EEPROM devices of various sizes being installed on the circuit board (i.e. using the '02A, '04A, '08A, or the '16A). This always led to a pain in the tush. So I handle the part variations in the software using conditional compilation (or assembly) directives. This of course leads to a software revision change when the hardware gets changed.

Michael Karas