Single-precision floating-point format: Difference between revisions

Revision as of 06:23, 31 May 2025

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'''Single-precision floating-point format''' (sometimes called '''FP32''' or '''float32''') is a [[computer number format]], usually occupying [[32 bits]] in [[computer memory]]; it represents a wide [[dynamic range]] of numeric values by using a [[floating point|floating radix point]].

A floating-point variable can represent a wider range of numbers than a [[fixed-point arithmetic|fixed-point]] variable of the same bit width at the cost of precision. A [[signedness|signed]] 32-bit [[integer]] variable has a maximum value of 2³¹ − 1 = 2,147,483,647, whereas an [[IEEE 754]] 32-bit base-2 floating-point variable has a maximum value of (2 − 2⁻²³) × 2¹²⁷ ≈ 3.4028235 × 1910³⁸. All integers with seven or fewer decimal digits, and any 2^''n'' for a whole number −149 ≤ ''n'' ≤ 127, can be converted exactly into an IEEE 754 single-precision floating-point value.

In the IEEE 754 [[standardization|standard]], the 32-bit base-2 format is officially referred to as '''binary32'''; it was called '''single''' in [[IEEE 754-1985]]. IEEE 754 specifies additional floating-point types, such as 64-bit base-2 ''[[double-precision floating-point format|double precision]]'' and, more recently, base-10 representations.