IEEE 754 Floats

In memory, an IEEE floating point number consists one sign bit, exponent bits and trailing mantissa bits.

• Half-precision f16:
• Single-precision f32: ,
• Double-precision f64: ,

Subsections

• floating-pointer normalization
• subnormal number

Bias in Exponents

The exponent is biased. The offset can be computed as

For example, for f32, it has an offset of , where ¹

Stored Exponent	Scaling	Meaning
0		Zero (if mantissa = 0), subnormal (otherwise)|
1
…	…
127
…	…
254
255	N/A	Infinity (if mantissa = 0), NaN (otherwise)

Similarly, f16 has a bias of and f64 has a bias of .

Related

• We can use bit operations to isolate sign bit, exponent bits, or mantissa bits

Reference

• IEEE 754 Floats - Algorithmica

Footnotes

1. c++ - What is a subnormal floating point number? - Stack Overflow ↩