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Concept# Bit array

Summary

A bit array (also known as bitmask, bit map, bit set, bit string, or bit vector) is an array data structure that compactly stores bits. It can be used to implement a simple set data structure. A bit array is effective at exploiting bit-level parallelism in hardware to perform operations quickly. A typical bit array stores kw bits, where w is the number of bits in the unit of storage, such as a byte or word, and k is some nonnegative integer. If w does not divide the number of bits to be stored, some space is wasted due to internal fragmentation.
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−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 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 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.
Although most machines are not able to address individual bits in memory, nor have instructions to manipulate single bits, each bit in a word can be singled out and manipulated using bitwise operations.

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A bit array (also known as bitmask, bit map, bit set, bit string, or bit vector) is an array data structure that compactly stores bits. It can be used to implement a simple set data structure. A bit array is effective at exploiting bit-level parallelism in hardware to perform operations quickly. A typical bit array stores kw bits, where w is the number of bits in the unit of storage, such as a byte or word, and k is some nonnegative integer. If w does not divide the number of bits to be stored, some space is wasted due to internal fragmentation.

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