Single-precision floating-point format is a computer number format that occupies 4 bytes (32 bits) in computer memory and represents a wide dynamic range of values by using a floating point.
In IEEE 754-2008 the 32-bit base 2 format is officially referred to as binary32. It was called single in IEEE 754-1985. In older computers, different floating-point formats of 4 bytes were used, e.g., GW-BASIC's single-precision data type was the 32-bit MBF floating-point format.
One of the first programming languages to provide single- and double-precision floating-point data types was Fortran. Before the widespread adoption of IEEE 754-1985, the representation and properties of the double float data type depended on the computer manufacturer and computer model.
Single-precision binary floating-point is used due to its wider range over fixed point (of the same bit-width), even if at the cost of precision. A signed32-bitinteger can have a maximum value of 231 - 1 = 2,147,483,647, whereas the maximum representable IEEE 754 floating point value is (2−2−23) × 2127 ≈ 3.402823 × 1038. All integers with six or fewer significant decimal digits can be converted to an IEEE 754 floating point value without loss of precision, some integers up to nine significant decimal digits can be converted to an IEEE 754 floating point value without loss of precision, but no more than nine significant decimal digits can be stored. As an example, the 32-bit integer 2,147,483,647 converts to 2,147,483,650 in IEEE 754 form.
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