E8M0 (OCP MX Scale) | Floating Point Format Guide

Bit Layout

Exponent

E

8 bits

E8M0 is all exponent. There is no sign bit and no mantissa field, so the entire 8-bit encoding is a biased exponent and every representable value is exactly 2^k.

Overview

E8M0 is the shared scale type of the OCP Microscaling (MX) Specification v1.0. An MX block is 32 elements of a narrow type (FP8 E4M3, FP8 E5M2, FP6, FP4 or MXINT8) plus one E8M0 scale that multiplies all of them. The narrow element type supplies precision; the shared scale supplies dynamic range.

Restricting the scale to an exact power of two is deliberate. Multiplying by 2^k is an exponent adjustment, not a multiply, so applying a block scale costs nothing in hardware and introduces no rounding error of its own.

E8M0 has no zero and no subnormals MX Table 7 lists Zeros as "N/A". Exponent field 0 is not reserved: it is the ordinary normal value 2^-127, the smallest magnitude the format can hold. There is also no infinity. The single reserved pattern is 11111111, which is NaN.

Encoding Rules

Every Value

value = 2^{(exponent - 127)}

Exponent fields 0 through 254 map to 2^-127 through 2¹²⁷, covering 255 binades with no gaps and no duplicates. That is the full supported exponent range MX Table 7 specifies, −127 to 127.

Special Values (MX Table 7)

NaN: the single pattern 11111111 (exponent field 255).
No Zero: there is no encoding for zero. A block that needs to be zero encodes that in its elements, not its scale.
No Subnormals: exponent field 0 is a normal value, so there is no gradual-underflow region.
No Infinity: overflow above 2¹²⁷ saturates to 2¹²⁷, or produces NaN if you select the non-saturating overflow behavior.
No Sign: a scale is always positive. Signs live in the elements.

Rounding acts on the exponent With no mantissa field there is nothing to round within a binade, so the rounding mode chooses between neighbouring powers of two instead. Encoding 1.5 under ties-to-even gives 2¹; under toward-zero it gives 2⁰.

Interactive Value Visualizer

Click any bit to flip it, drag the slider, or enter a decimal or hex value. The graph shows how values are distributed across the encoding space.

Decimal:

Hex:

Dynamic Range & Precision

Property	Value
Max Positive (Normal)	1.701411835e+38
Min Positive (Normal)	5.877471754e-39
Subnormals	N/A (no subnormal encodings)
Zero	N/A (no zero encoding)
Machine Epsilon (at 1.0)	1
Approx. Decimal Digits	~0.0
Exponent Bias	127
Exponent Range	2^-127 to 2^127
Total Bit Patterns	256
Supports Infinity	No
Supports NaN	Yes

Special Values & Bit Patterns

Value	Bit Pattern	Decimal
Min Normal	00000000	5.877471754e-39
Max Normal	11111110	1.701411835e+38
NaN	11111111	NaN

Format Comparison

Property	E8M0	FP8 E4M3	FP8 E5M2	FP4 E2M1
Total Bits	8	8	8	4
Sign Bits	0	1	1	1
Exponent Bits	8	4	5	2
Mantissa Bits	0	3	2	1
Bias	127	7	15	1
Max Value	1.701411835e+38	448	57344	6
Min Normal	5.877471754e-39	0.015625	0.00006103515625	1
Epsilon	1	0.125	0.25	0.5
~Decimal Digits	~0.0	~0.9	~0.6	~0.3
Has Infinity	No	No	Yes	No
Has NaN	Yes	Yes	Yes	No
Has Subnormals	No	Yes	Yes	Yes

Where E8M0 Is Used

OCP Microscaling blocks: the OCP MX Spec v1.0 uses one E8M0 scale per 32-element block for MXFP8, MXFP6, MXFP4 and MXINT8.
NVIDIA Blackwell: the PTX ISA exposes block-scaled MMA instructions whose scale operand is an E8M0 byte.
ML frameworks: the ml_dtypes library provides float8_e8m0fnu as a NumPy dtype extension, and PyTorch exposes torch.float8_e8m0fnu for MX scaling.
Microscaling research: the Microscaling Data Formats for Deep Learning paper introduces the shared-scale design that MX standardizes.