Float Exposed – fp4 / fp6 / fp8 / fp16 / bf16 / fp32

Value

Bit Pattern

All Non‑negative Values (log₂ axis → relative precision; each column is one binade)

All Bit Patterns

zerosubnormalnormalinfNaN

Evaluation in Base‑2

Evaluation in Base‑10

Exact Base‑10 Value

Round‑trip Interval (inputs that round to this value)

Delta to Next/Previous Representable Value

Delta to Next Representable Value

Delta to Previous Representable Value

References

Exposing Floating Point — Bartosz Ciechanowski. Interactive article on how the sign, exponent and mantissa bits form a value, subnormals, rounding and precision.
float.exposed — Bartosz Ciechanowski. Interactive bit-level explorer for fp16 / bf16 / fp32 / fp64; the layout and interaction design of this page are borrowed from it.
jax-ml/ml_dtypes — Reference implementation of fp4 / fp6 / fp8 formats used to verify every encoding and rounding rule on this page.
OCP Microscaling Formats (MX) Specification v1.0 — Defines the E2M1 / E2M3 / E3M2 / E4M3 / E5M2 element formats.
FP8 Formats for Deep Learning — Micikevicius et al., 2022. Proposal of the E4M3 and E5M2 formats.
IEEE 754-2019 — Standard for binary16 / binary32 / binary64 encoding and rounding.