Single precision
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In computing, single precision is a computer numbering format that occupies one storage location in computer memory at a given address. A single-precision number, sometimes simply a single, may be defined to be an integer, fixed point, or floating point.
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: 24The format is written with an implicit most-significant bit with value 1 unless the written exponent is all zeros. Thus only 23 bits of the fraction appear in the memory format but the total precision is 24 bits.
syyy yyyy yxxx xxxx xxxx xxxx xxxx xxxx (23 xs)
Exponent encodings
Emin (0x01) = -126 Emax (0x7f) = 127 Exponent bias (0x7f) = 127The true exponent = written exponent - exponent bias
0x00 and 0xff are reserved exponents 0x00 is used to represent zero and denormals 0xff is used to represent infinity and NaNsAll bit patterns are valid encodings.
Single precision examples in
3f80 0000 = 1
c000 0000 = -2
7f7f 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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