Data+Representation

=Floating Point Numbers=

Floating point numbers are used to represent very large and very small numbers. They are represented with a **mantissa** and an **exponent**. The mantissa represents the actual values and the exponent is the value of the power of 2, the mantissa is in. (eg. for 0.11 x2^10, 0.11 is the mantissa and 10 is the exponent).

When floating point binary is used it is **normalised**. In normalised binary, positive number must start with 0.1...and the exponent must be converted to 2's complement if it is negative. Negative numbers must be converted to 2's complement form (so the mantissa must start with 1.0.... )

The accuracy and range of numbers that can be represented depends on the amount of bits used for the mantissa and exponent. This means the biggest and smallest possible numbers stored will vary depending on the amount of bits used for each (although it will never be possible to store 0 in normalised binary). For example increasing the number of bits for the exponent would reduce the number of bits available for the mantissa, so the accuracy available is reduced, but the range of numbers that can be used is increased.