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Dotted decimal notation is a system of presenting numbers that is a little different from the common conventions in arithmetic as it is taught in schools. Specifically, dotted decimal notation is used in various IT contexts, including in Internet Protocol addresses.
At its core, dotted decimal notation is just another way of recording and displaying a big number. It is a particular method of notation that can replace "octets" or sets bytes (eight individual bits) in machine language. Dotted decimal notation effectively puts numbers in different containers that are separated by dots or decimals.
In changing a set of bytes into dotted decimal notation, the ones and zeros making up the bite of information are enumerated into decimal-delineated numbers between 0 and 255. In IP version 4 addresses, which are 32 bits long, this results in four numbers, for example: 0.0.172.1
The dotted decimal notation system used so commonly in IP addressing is just one of several choices for representing numbers differently. Another common one is the hexadecimal system, in which traditional numbers are augmented by letters of the alphabet in a base-16 system.