Dot-decimal notation is a presentation format for numerical data. It consists of a string of decimal numbers, each pair separated by a full stop (dot).
A common use of dot-decimal notation is in information technology where it is a method of writing numbers in octet-grouped base-10 (decimal) numbers separated by dots (full stops). In computer networking, Internet Protocol Version 4 addresses are commonly written using the quad-dotted notation of four decimal integers, ranging from 0 to 255 each.
Definition and use
Dot-decimal notation is a presentation format for numerical data expressed as a string of decimal numbers each separated by a full stop. In computer networking, the term is often used as a synonym of dotted quad notation, or quad-dotted notation, a specific use to represent Internet Protocol Version 4 addresses. 
For example, the hexadecimal number 0xFF0000 may be expressed in dot-decimal notation as 255.0.0.
An Internet Protocol Version 4 (IPv4) address has 32 bits. For purposes of representation, the bits may be divided into four octets written in decimal numbers, ranging from 0 to 255, concatenated as a character string with full stop delimiters between each number.
For example, the address of the loopback interface, usually assigned the host name localhost, is 127.0.0.1. It consists of the four octets, written in binary notation: 01111111, 00000000, 00000000, and 00000001.
No formal specification of this textual IP address representation exists. The first mention of this format in RFC documents was in RCF 780 for the Mail Transfer Protocol of May 1981, in which the IP address was supposed to be enclosed in brackets. And an alternate representation was a decimal integer prefixed by a pound sign. A table in RFC 790 (Assigned Numbers) used the dotted decimal format, zero-padding each number to three digits.
A popular implementation of IP networking, originating in 4.2BSD, contains a function inet_aton() for converting IP addresses in character string representation to internal binary storage. In addition to the basic four-decimals format and full 32-bit addresses, it also supported intermediate syntax forms of octet.24bits (e.g. 10.1234567; for Class A addresses) and octet.octet.16bits (e.g. 172.16.12345; for Class B addresses). It also allowed the numbers to be written in hexadecimal and octal, by prefixing them with 0x and 0, respectively. These features continue to be supported by software until today, even though they are seen as non-standard. But this also means addresses where an IP address component is written with a leading zero digit may be interpreted differently by different programs: some will ignore the leading zero, some will interpret the number as octal.
IP addresses in the dot-decimal notation are also presented in CIDR notation, in which the IP address is suffixed with a slash and a number, used to specify the length of the associated routing prefix. For example, 127.0.0.1/8 specifies that the IP address has an 8-bit routing prefix, and therefore the subnet mask 255.0.0.0.
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- Main, Andrew (23 February 2005). Textual Representation of IPv4 and IPv6 Addresses. IETF. I-D draft-main-ipaddr-text-rep-02. https://tools.ietf.org/html/draft-main-ipaddr-text-rep-02.
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