leastsignificantbit

The least significant bit (LSB) is the rightmost bit in the binary representation of an integer, corresponding to the value 2^0, or 1. It has the smallest weight among the bits in the word, and flipping it changes the value by one. For unsigned integers, the LSB determines parity: a number is even if the LSB is 0 and odd if it is 1.

In practice, the LSB can be accessed by x mod 2 or by the bitwise operation x & 1. Shifting right by one bit (x >> 1) discards the LSB and halves the value; shifting left (x << 1) moves bits toward more significant positions and inserts zeros at the LSB in most languages.

Common bit tricks involve the LSB. The expression x & -x isolates the least significant 1 bit of x, while (x & (x - 1)) clears the least significant 1 bit. These techniques are frequently used in low-level algorithms, such as bit counting and sparse set operations.

Applications of the LSB span data encoding and processing. Parity checks in data transmission use the LSB to detect single-bit errors. LSB steganography embeds data by modifying the least significant bits of image or audio samples, aiming to minimize perceptual changes. In hardware and software, the LSB concept underpins bitwise arithmetic, masking, and efficient algorithms for manipulating binary data.

Notes: the meaning of the LSB depends on the representation; in multi-byte words, endianness concerns byte order in memory rather than the intrinsic significance of a single bit. Example: 13 in binary is 1101, so the LSB is 1; 12 is 1100, so the LSB is 0.