Floating Point

(fraction representation)

Further explanation can be found at http://www.research.microsoft.com/~hollasch/cgindex/coding/ieeefloat.html

and at http://wwweng.murdoch.edu.au/sunws/html_docs/common-tools/numerical_comp_guide/index.html

Large numbers need to be represented by Floating Point.

Mantissa	Exponent
135.2675	08	135.2675 x 10⁸	= 13 526 750 000
3.12	-02	3.12 x 10^-2	= 0.0312

Scientific Notation is a special floating point representation.

The Mantissa must be greater than 1 and less than 10.

This means that the digit in front of the decimal point must be 1,2,3,4,5,6,7,8 or 9.

Floating Point numbers can also be called REAL NUMBERS in computer terms. However, there are more real numbers than can be represented by floating point eg π or e.

The single precision version of the IEEE 754-1985 standard uses 32 bits.

0 00000000 1 000 0000 0000 0000 0000 0000

0 this is the sign bit 0 is + and 1 is –

00000000 these eight bits are for the exponent 11111110 is the highest number

1 is the hidden bit. It is always 1.

000 0000 0000 0000 0000 0000 the remaining 23 bits are the fractional part of the mantissa

This can also be written as

S EEEE EEEE 1 FFF FFFF FFFF FFFF FFFF FFFF

= ±2^{(EEEE EEEE} ^-01111111)x 1. FFF FFFF FFFF FFFF FFFF FFFF

= ±2^(E-127)x 1. F

There is a conversion site at http://babbage.cs.qc.edu/courses/cs341/IEEE-754.html