bittisarjat

Bittisarjat is the Finnish term for sequences of bits, i.e., finite strings over the binary alphabet {0,1}. In information theory, computing, and digital communication, bit strings are used to represent data, instructions, and signals. A bitstring of length n is written as b1b2…bn, where each bi is either 0 or 1. The set of all bitstrings of length n is denoted {0,1}^n, and the set of all finite binary strings is {0,1}*, with the empty string acting as the identity under concatenation.

Formally, bitstrings form a free monoid under concatenation. The operation of combining two strings is concatenation, and the empty string serves as the neutral element. Common properties include length (n), Hamming weight (the number of 1s in the string), and Hamming distance (the number of positions where two strings differ). Prefixes, suffixes, and cyclic shifts are also studied in sequence analysis.

Bitstrings are used to encode numerical values (binary representation), data blocks, and control information in storage and transmission systems. They also underpin error detection and correction schemes, such as parity bits and error-correcting codes, where codewords are designed bitstrings with desirable properties. Counting aspects are fundamental: there are 2^n bitstrings of length n, and the total set {0,1}* is infinite.

In programming and data structures, bit strings appear as bit arrays or bitsets, enabling efficient storage and bitwise operations (AND, OR, XOR). Related topics include binary codes, information theory, and coding theory.