The IEEE-754 Standard

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating point implementations that made them difficult to use reliably and portably. It specifies interchange and arithmetic formats and methods for binary and decimal floating-point arithmetic in computer programming environments. Nowadays many hardware floating point units use the IEEE 754 standard.

This standard was needed because with Integers or with Binary numbers it was impossible to represent floating (decimal) point. For example wit Integers we can represent 5 and 6 but not 5.5 or 5.25. There were many tries to represent those numbers but almost everyone was using something different. Here comes the standard in play. Since it was established it became the universal representation for floating points.

The newest and current version is IEEE 754-2008 and it was published in August 2008, however it includes nearly all of the original IEEE 754-1985 standard floating point arithmetics.

IEEE 754 represents numbers in 32 bits or 4 bytes. The first bit is reserved for the sign of the number (either positive or negative). The next 8 bits are for the Exponent and the last 23 bits are for the Mantissa.

An interesting fact is that the IEEE-754 standard contains two values for 0. They are -0 and +0.

Read more about IEEE-754 at Wikipedia