Single precision

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In computing, single precision is a computer numbering format that occupies one storage location in computer memory at address. A single-precision number, sometimes simply a single, may be defined to be an integer, fixed point, or floating point.

Pedantic usage note: When using single-precision as an adjective, as in single-precision number, hyphenate it. When using it as a noun ("Double precision differs from single precision."), do not hyphenate it.

Modern computers with 32-bit stores (single precision) provide 64-bit double precision. Single precision floating point is an IEEE 754 standard for encoding floating point numbers that uses 4 bytes.

Contents

Single precision memory format

 Sign bit: 1
 Exponent width: 8  
 Significand precision: 24   

The format is written with an implicit integer bit with value 1 unless the written exponent is all zeros. Thus only 23 bits of the fraction appear in the memory format.

 syyy yyyy yxxx xxxx xxxx xxxx xxxx xxxx (23 xs)

Exponent encodings

 Emin (0x01) = -126
 Emax (0x7e) = 127
 Exponent bias (0x3f) = 127

The true exponent = written exponent - exponent bias

 0x00 and 0x7f  are reserved exponents 
 0x00 is used to represent zero and denormals
 0x7f is used to represent infinity and NaNs

All bit patterns are valid encodings.

Single precision examples in hexadecimal

 3f80 0000   = 1
 c000 0000   = -2
 7fef ffff   ~ 3.4028234 x 1038  (Max Single)
 3eaa aaaa   ~ 1/3

(1/3 rounds up instead of down like double precision, because of the even number of bits in the significand.)

 0000 0000   = 0
 8000 0000   = -0
 7f80 0000   = Infinity
 ff80 0000   = -Infinity

See also

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