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# Half-precision floating-point number format

The half-precision floating-point formats available are `ieee` and `alternative`. In both formats, the basic layout of the 16-bit number is the same.

The half-precision floating-point format is as follows:

Figure 5-1 Half-precision floating-point format

Where:

```   S (bit):      Sign bit
E (bits[14:10]):  Biased exponent
T (bits[9:0]):    Mantissa.
```

The meanings of these fields depend on the format that is selected.

The IEEE half-precision format is as follows:

```IF E==31:
IF T==0: Value = Signed infinity
IF T!=0: Value = Nan
T determines Quiet or Signalling:
0: Quiet NaN
1: Signalling NaN
IF 0<E<31:
Value = (-1)^S x 2^(E-15) x (1 + (2^(-10) x T))
IF E==0:
IF T==0: Value = Signed zero
IF T!=0: Value = (-1)^S x 2^(-14) x (0 + (2^(-10) x T))
```

The alternative half-precision format is as follows:

```IF 0<E<32:
Value = (-1)^S x 2^(E-15) x (1 + (2^(-10) x T))
IF E==0:
IF T==0: Value = Signed zero
IF T!=0: Value = (-1)^S x 2^(-14) x (0 + (2^(-10) x T))
```