Loading AI tools

Convention to identify bit positions From Wikipedia, the free encyclopedia

In computing, **bit numbering** is the convention used to identify the bit positions in a binary number.

In computing, the **least significant bit** (**LSb**) is the bit position in a binary integer representing the binary 1s place of the integer. Similarly, the **most significant bit** (**MSb**) represents the highest-order place of the binary integer. The LSb is sometimes referred to as the *low-order bit* or *right-most bit*, due to the convention in positional notation of writing less significant digits further to the right. The MSb is similarly referred to as the *high-order bit* or *left-most bit*. In both cases, the LSb and MSb correlate directly to the least significant digit and most significant digit of a decimal integer.

Bit indexing correlates to the positional notation of the value in base 2. For this reason, bit index is not affected by how the value is stored on the device, such as the value's byte order. Rather, it is a property of the numeric value in binary itself. This is often utilized in programming via bit shifting: A value of `1 << `

corresponds to the *n**n*^{th} bit of a binary integer (with a value of `2`

).^{n}

In digital steganography, sensitive messages may be concealed by manipulating and storing information in the least significant bits of an image or a sound file. The user may later recover this information by extracting the least significant bits of the manipulated pixels to recover the original message. This allows the storage or transfer of digital information to remain concealed.

A diagram showing how manipulating the least significant bits of a color can have a very subtle and generally unnoticeable affect on the color. In this diagram, green is represented by its RGB value, both in decimal and in binary. The red box surrounding the last two bits illustrates the least significant bits changed in the binary representation.

This table illustrates an example of decimal value of 149 and the location of LSb. In this particular example, the position of unit value (decimal 1 or 0) is located in bit position 0 (n = 0). MSb stands for *most significant bit*, while LSb stands for *least significant bit*.

Binary (Decimal: 149) | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
---|---|---|---|---|---|---|---|---|

Bit weight for given bit position n ( 2^{n} ) |
2^{7} |
2^{6} |
2^{5} |
2^{4} |
2^{3} |
2^{2} |
2^{1} |
2^{0} |

Bit position label | MSb | LSb |

The expressions *most significant bit first* and *least significant bit at last* are indications on the ordering of the sequence of the bits in the bytes sent over a wire in a serial transmission protocol or in a stream (e.g. an audio stream).

*Most significant bit first* means that the most significant bit will arrive first: hence e.g. the hexadecimal number `0x12`

, `00010010`

in binary representation, will arrive as the sequence `0 0 0 1 0 0 1 0`

.

*Least significant bit first* means that the least significant bit will arrive first: hence e.g. the same hexadecimal number `0x12`

, again `00010010`

in binary representation, will arrive as the (reversed) sequence `0 1 0 0 1 0 0 0`

.

When the bit numbering starts at zero for the least significant bit (LSb) the numbering scheme is called *LSb 0*.^{[1]} This bit numbering method has the advantage that for any unsigned number the value of the number can be calculated by using exponentiation with the bit number and a base of 2.^{[2]} The value of an unsigned binary integer is therefore

where *b _{i}* denotes the value of the bit with number

When the bit numbering starts at zero for the most significant bit (MSb) the numbering scheme is called *MSb 0*.

The value of an unsigned binary integer is therefore

LSb of a number can be calculated with time complexity of with formula , where means bitwise operation *AND* and means bitwise operation *NOT on* *.*

For MSb 1 numbering, the value of an unsigned binary integer is

PL/I numbers `BIT` strings starting with 1 for the leftmost bit.

The Fortran `BTEST` function uses LSb 0 numbering.

Seamless Wikipedia browsing. On steroids.

Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.

Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.