Editing Computer number format (section)

==Binary number representation==
{{See also|Integer (computer science)}}
Computers represent data in sets of binary digits.  The representation is composed of bits, which in turn are grouped into larger sets such as bytes.

{| class="wikitable" style="float: right; clear:right; margin-left:1em; text-align:right;"
|+ Table 1: Binary to octal
|-
! Binary string !! Octal value
|-
| 000 || 0
|-
| 001 || 1
|-
| 010 || 2
|-
| 011 || 3
|-
| 100 || 4
|-
| 101 || 5
|-
| 110 || 6
|-
| 111 || 7
|}

{| class="wikitable" style="float: right; clear:right; margin-left:1em; text-align:right;"
|+ Table 2: Number of values for a bit string.
|-
! Length of bit string (b) !! Number of possible values (N)
|-
| 1 || 2
|-
| 2 || 4
|-
| 3 || 8
|-
| 4 || 16
|-
| 5 || 32
|-
| 6 || 64
|-
| 7 || 128
|-
| 8 || 256
|-
| 9 || 512
|-
| 10 || 1024
|-
| ... || 
|-
| <math>b</math> || <math>2^b=N</math>
|}

A ''[[bit]]'' is a [[Binary numeral system|binary]] [[Numerical digit|digit]] that represents one of two [[state (computer science)|states]].  The concept of a bit can be understood as a value of either ''1'' or ''0'', ''on'' or ''off'', ''yes'' or ''no'', ''true'' or ''false'', or [[encoding|encoded]] by a switch or [[Toggle switch|toggle]] of some kind.

While a single bit, on its own, is able to represent only two values, a [[Bit string|string of bits]] may be used to represent larger values.  For example, a string of three bits can represent up to eight distinct values as illustrated in Table 1.

As the number of bits composing a string increases, the number of possible ''0'' and ''1'' combinations increases [[Exponentiation|exponentially]].  A single bit allows only two value-combinations, two bits combined can make four separate values, three bits for eight, and so on, increasing with the formula 2<sup>n</sup>.  The amount of possible combinations doubles with each binary digit added as illustrated in Table 2.

Groupings with a specific number of bits are used to represent varying things and have specific names.

A ''[[byte]]'' is a bit string containing the number of bits needed to represent a [[Character (computing)|character]].  On most modern computers, this is an eight bit string.  Because the definition of a byte is related to the number of bits composing a character, some older computers have used a different bit length for their byte.<ref>{{cite web|title=byte definition|url=http://catb.org/~esr/jargon/html/B/byte.html|access-date=24 April 2012}}</ref>  In many [[Computer Architecture|computer architectures]], the byte is the smallest [[Byte addressing|addressable unit]], the atom of addressability, say.<!-- Find an external source for this -->  For example, even though 64-bit processors may address memory sixty-four bits at a time, they may still split that memory into eight-bit pieces.  This is called byte-addressable memory.  Historically, many [[CPU core voltage|CPUs]] read data in some multiple of eight bits.<ref>{{cite web|title=Microprocessor and CPU (Central Processing Unit)|url=http://www.networkdictionary.com/hardware/mc.php|publisher=Network Dictionary|access-date=1 May 2012|archive-url=https://web.archive.org/web/20171003225434/http://www.networkdictionary.com/hardware/mc.php|archive-date=3 October 2017|url-status=dead}}</ref>  Because the byte size of eight bits is so common, but the definition is not standardized, the term [[Octet (computing)|octet]] is sometimes used to explicitly describe an eight bit sequence.

A ''[[nibble]]'' (sometimes ''nybble''), is a number composed of four bits.<ref>{{cite web|title=nybble definition|url=http://catb.org/~esr/jargon/html/N/nybble.html|access-date=3 May 2012}}</ref>  Being a [[half-byte]], the nibble was named as a play on words.  A person may need several nibbles for one bite from something; similarly, a nybble is a part of a byte.  Because four bits allow for sixteen values, a nibble is sometimes known as a [[hexadecimal digit]].<ref>{{cite web|title=Nybble|url=http://www.techterms.com/definition/nybble|publisher=TechTerms.com|access-date=3 May 2012}}</ref>