# Single precision

(Redirected from Single-precision)

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.

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## 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
```

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