A number whose powers are used to represent other numbers (e.g. base 10 = decimal representation)

Numbers are usually represented in Positional Notation, with a common base like 2, 10 or 16. A common topic is conversion between representations in different bases.

Examples of base number systems:

  • Base 2, binary has digits 0 and 1
  • Base 8, octal has digits 0 - 7
  • Base 10, denary has the digits 0 - 9.
  • Base 16, hex has the digits 0 - 9 and the letters A - F

To convert between bases you split up the number into powers of n, where n is the base number:

  • 300 = 1* 16^2 + 2* 16^1 + 12* 16^0

    So the denary number 300 in base 16 (hex) is 12C

  • 20 = 1* 2^4 + 0* 2^3 + 1* 2^2 + 0* 2^1 + 0* 2^0

    So the denary number 20 in base 2 (binary) is 10100

Some completely different meanings for "base" are [ base-class] and [ base-address].