Numbering Systems 

Numbering systems are characterized by their base number. For example the famous decimal system (base 10) and its 10 different digits,

In general a numbering system with a base r will have r different digits (including the 0) in its number set. These digits will range from 0 to r-1,

The most widely used numbering systems are listed in the table below:

Numbering SystemBaseDigits Set
Binary21 0
Octal87 6 5 4 3 2 1 0
Decimal109 8 7 6 5 4 3 2 1 0
Hexadecimal16F E D C B A 9 8 7 6 5 4 3 2 1 0


The correspondence between numbers with different bases is illustrated in the collapsible note below:

 Correspondence between digits for the different numbering systems


The base of a number is usually specified as a subscript, e.g.:
  1. (01000011)2,
  2. (71203)8,
  3. (FF078ABC)16, ...etc.


Or a letter indicating the base (d for decimal, b for binary, o for octal and h for hexadecimal) is appended to the number, e.g.:
  1. 01000011b,
  2. 71203o,
  3. FF078ABCh, ...etc.