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Repair Windows errors before they cause bigger problemsFix Now →Scan for outdated or missing drivers - takes under a minuteDriver Scan →The least significant bit (LSB) is the rightmost bit in an ordered bit string. In ordinary binary notation for an unsigned integer, it occupies the 20 place, so it contributes either zero or one to the number’s value.
What does “least significant bit” mean?
A bit is a binary digit—0 or 1—and a bit string is an ordered sequence of bits. NIST defines the least significant bit or bits as “the right-most bit(s) of a bit string.” In that written convention, the leftmost bit is the most significant and the rightmost is the least significant.
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For example, in the four-bit string 0101, the LSB is the final 1. Read as a four-bit unsigned binary integer, 0101 equals five.
Why is the rightmost bit least significant?
Binary integers use positional place values. In the representation b3b2b1b0, the positions from left to right carry weights 23, 22, 21, and 20. The rightmost bit, b0, has the smallest weight. Its contribution to the total is its value multiplied by 20, which is 1. A NIST-hosted explanation likewise identifies b0 as least significant because it corresponds to the lowest power of two.
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For instance, 11012 has an LSB of 1, contributing 1 × 20 = 1; the full value is 13. In 11002, the LSB is 0, so that position contributes zero.
Does LSB always mean the first bit stored or transmitted?
No. “Rightmost” describes a bit’s position in the stated written bit string, while storage and transmission order depend on the representation or protocol. Endianness describes ordering conventions for bytes; NIST also notes that big-endian can apply to bit strings. Do not infer from the term LSB alone which bit is sent first or where it is stored. Name the format or protocol when discussing those implementation details. See NIST’s entries on byte order and big-endian.
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How is LSB used for floating-point numbers?
The term can refer to a component field rather than the final bit of an entire encoded word. For a nonzero normalized binary floating-point machine number, NIST’s Digital Library of Mathematical Functions writes the significand as b0.b1…bp−1 and identifies bp−1 as the significand’s least significant bit. When interpreting a format, specify whether LSB refers to the significand, another field, or a complete bit string.
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