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The basic unit of digital storage is called a bit. In most common architectures, 8 bits are grouped together to form a byte. Byte addressable memory refers to data which can be accessed 8 bits at a time, irrespective of the width of the data and address buses.
Many of the common architectures can address more than 8 bits of data at a time. For example, the Intel 386SX processor can handle 16 bit data, i.e. two bytes. Data is transferred over a 16 bit bus. But data in memory may be of various lengths. A 64-bit architecture machine might still need to access byte sized data over it's 64 bit address line. Such memory, which is accessible 8 bits at a time is called Byte-Addressable Memory.