Bit-length or bit width is the number of binary digits, called
bit
The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
s, necessary to represent an unsigned
integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...
as a
binary number. Formally, the bit-length of a natural number
is
:
where
is the
binary logarithm and
is the ceiling function.
At their most fundamental level, digital computers and telecommunications devices (as opposed to
analog
Analog or analogue may refer to:
Computing and electronics
* Analog signal, in which information is encoded in a continuous variable
** Analog device, an apparatus that operates on analog signals
*** Analog electronics, circuits which use analog ...
devices) process data that is encoded in
binary
Binary may refer to:
Science and technology Mathematics
* Binary number, a representation of numbers using only two digits (0 and 1)
* Binary function, a function that takes two arguments
* Binary operation, a mathematical operation that ta ...
format. The binary format expresses data as an arbitrary length series of values with one of two choices: Yes/No, 1/0, True/False, etc., all of which can be expressed electronically as On/Off. For information technology applications, the amount of information being processed is an important design consideration. The term bit-length is technical shorthand for this measure.
For example,
computer processors are often designed to process data grouped into
words
A word is a basic element of language that carries an objective or practical meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no conse ...
of a given length of bits (8 bit, 16 bit, 32 bit, 64 bit, etc.). The bit-length of each word defines, for one thing, how many memory locations can be independently addressed by the processor. In
public-key cryptography
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic alg ...
,
keys are defined by their length expressed in binary digits - their bit length.
References
{{Reflist
Binary arithmetic
Computer arithmetic