128-bit computingGeneral home computing and gaming utility emerge at 8-bit (but not at 1-bit or 4-bit) word sizes, as 28=256 words become possible. Thus, early 8-bit CPUs (TRS 80, 6502, Intel 8088 introduced 1976-1981 by Commodore, Tandy Corporation, Apple and IBM) inaugurated the era of personal computing. Many 16-bit CPUs already existed in the mid-1970's. Over the next 30 years, the shift to 16-bit, 32-bit and 64-bit computing allowed, respectively, 216=65,536 unique words, 232=4,294,967,296 unique words and 264=18,446,744,073,709,551,615 unique words respectively, each step offering a meaningful advantage until 64 bits was reached.
Dot productIn mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more).
