Least significant bit

# Least significant bit

Discussion
 Ask a question about 'Least significant bit' Start a new discussion about 'Least significant bit' Answer questions from other users Full Discussion Forum

Encyclopedia
In computing
Computing
Computing is usually defined as the activity of using and improving computer hardware and software. It is the computer-specific part of information technology...

, the least significant bit (lsb) is the bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

position in a binary
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

giving the units value, that is, determining whether the number is even or odd. The lsb is sometimes referred to as the right-most bit, due to the convention in positional notation
Positional notation
Positional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations for its use of the same symbol for the different orders of magnitude...

of writing less significant digits further to the right. It is analogous to the least significant digit
Numerical digit
A digit is a symbol used in combinations to represent numbers in positional numeral systems. The name "digit" comes from the fact that the 10 digits of the hands correspond to the 10 symbols of the common base 10 number system, i.e...

of a decimal
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

integer, which is the digit in the ones (right-most) position.http://support.microsoft.com/kb/130861

It is common to assign each bit a position number, ranging from zero to N-1, where N is the number of bits in the binary representation used. Normally, this is simply the exponent for the corresponding bit weight in base-2 (such as in `231..20`). Although a few CPU manufacturers assign bit numbers
Bit numbering
In computing, bit numbering is the convention used to identify the bit positions in a binary number or a container for such a value...

the opposite way (which is not the same as different endianness
Endianness
In computing, the term endian or endianness refers to the ordering of individually addressable sub-components within the representation of a larger data item as stored in external memory . Each sub-component in the representation has a unique degree of significance, like the place value of digits...

), the term lsb (of course) remains unambiguous as an alias for the unit bit.

By extension, the least significant bits (plural) are the bits of the number closest to, and including, the lsb.

The least significant bits have the useful property of changing rapidly if the number changes even slightly. For example, if 1 (binary 00000001) is added to 3 (binary 00000011), the result will be 4 (binary 00000100) and three of the least significant bits will change (011 to 100). By contrast, the three most significant bits
Most significant bit
In computing, the most significant bit is the bit position in a binary number having the greatest value...

stay unchanged (000 to 000).

Least significant bits are frequently employed in pseudorandom number generator
Pseudorandom number generator
A pseudorandom number generator , also known as a deterministic random bit generator , is an algorithm for generating a sequence of numbers that approximates the properties of random numbers...

s, hash function
Hash function
A hash function is any algorithm or subroutine that maps large data sets to smaller data sets, called keys. For example, a single integer can serve as an index to an array...

s and checksum
Checksum
A checksum or hash sum is a fixed-size datum computed from an arbitrary block of digital data for the purpose of detecting accidental errors that may have been introduced during its transmission or storage. The integrity of the data can be checked at any later time by recomputing the checksum and...

s.

## Least significant byte

LSB (lsb) can also stand for least significant byte. The meaning is parallel to the above: it is the byte
Byte
The byte is a unit of digital information in computing and telecommunications that most commonly consists of eight bits. Historically, a byte was the number of bits used to encode a single character of text in a computer and for this reason it is the basic addressable element in many computer...

(or octet
Octet (computing)
An octet is a unit of digital information in computing and telecommunications that consists of eight bits. The term is often used when the term byte might be ambiguous, as there is no standard for the size of the byte.-Overview:...

) in that position of a multi-byte number which has the least potential value.

• Most significant bit
Most significant bit
In computing, the most significant bit is the bit position in a binary number having the greatest value...

• Binary numeral system
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

• Signed number representations
Signed number representations
In computing, signed number representations are required to encode negative numbers in binary number systems.In mathematics, negative numbers in any base are represented by prefixing them with a − sign. However, in computer hardware, numbers are represented in binary only without extra...

• Two's complement
Two's complement
The two's complement of a binary number is defined as the value obtained by subtracting the number from a large power of two...

• Bit numbering
Bit numbering
In computing, bit numbering is the convention used to identify the bit positions in a binary number or a container for such a value...

• Endianness
Endianness
In computing, the term endian or endianness refers to the ordering of individually addressable sub-components within the representation of a larger data item as stored in external memory . Each sub-component in the representation has a unique degree of significance, like the place value of digits...

• Binary logarithm
Binary logarithm
In mathematics, the binary logarithm is the logarithm to the base 2. It is the inverse function of n ↦ 2n. The binary logarithm of n is the power to which the number 2 must be raised to obtain the value n. This makes the binary logarithm useful for anything involving powers of 2,...

• Unit in the last place
Unit in the Last Place
In computer science and numerical analysis, unit in the last place or unit of least precision is the spacing between floating-point numbers, i.e., the value the least significant bit represents if it is 1...