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.

Single precision memory format

The 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

E_min (0x01) = -126 E_max (0x7f) = 127 Exponent bias (0x7f) = 127 The 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 NaNs

All bit patterns are valid encodings.

Single precision examples in hexadecimal

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

• half precision – single precision – double precision – quad precision
• Floating point

Computer arithmetic

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