Editing Bit array (section)

== Definition ==
A bit array is a mapping from some domain (almost always a range of integers) to values in the set {0, 1}. The values can be interpreted as dark/light, absent/present, locked/unlocked, valid/invalid, et cetera. The point is that there are only two possible values, so they can be stored in one bit. As with other arrays, the access to a single bit can be managed by applying an index to the array. Assuming its size (or length) to be ''n'' bits, the array can be used to specify a subset of the domain (e.g. {0, 1, 2, ..., ''n''&minus;1}), where a 1-bit indicates the presence and a 0-bit the absence of a number in the set. This set data structure uses about ''n''/''w'' words of space, where ''w'' is the number of bits in each [[Word (computer architecture)|machine word]]. Whether the least significant bit (of the word) or the most significant bit indicates the smallest-index number is largely irrelevant, but the former tends to be preferred (on [[Endianness|little-endian]] machines).

A finite [[binary relation]] may be represented by a bit array called a [[logical matrix]]. In the [[calculus of relations]], these arrays are composed with [[matrix multiplication]] where the arithmetic is Boolean, and such a composition represents [[composition of relations]].<ref>[[Irving Copilowish]] (December 1948) "Matrix development of the calculus of relations", [[Journal of Symbolic Logic]] 13(4): 193–203 [https://www.jstor.org/stable/2267134?seq=1#page_scan_tab_contents Jstor link]</ref>