How is a half-precision float laid out?

It uses 16 bits: 1 sign bit, then a 5-bit biased exponent, then a 10-bit mantissa. The exponent bias is 15, so a stored exponent of 15 represents 2^0. Normal numbers have an implicit leading 1 in the mantissa.

What is the value formula for a normal number?

For a normal half, the value is (-1)^sign times 1.mantissa times 2 to the power (exponent minus 15). The 1. is the implicit leading bit and the mantissa supplies the fractional part in 10 bits.

How are subnormals handled?

When the stored exponent is all zeros and the mantissa is non-zero, the number is subnormal: the implicit leading bit becomes 0 and the effective exponent is fixed at the minimum, -14. This lets half precision represent values closer to zero, with reduced precision.

What do infinity and NaN look like in bits?

An all-ones exponent with a zero mantissa is positive or negative infinity depending on the sign bit. An all-ones exponent with a non-zero mantissa is NaN. The tool detects and labels both.

What is the range and precision of float16?

Half precision covers roughly plus or minus 65504 as its largest finite magnitude, with about 3 to 4 significant decimal digits. It is common in machine learning and graphics where memory and bandwidth matter more than full float32 precision.

What is the IEEE-754 Float16 (Half) Inspector?

Decode any 16-bit IEEE-754 half-precision float into its sign, 5-bit exponent, and 10-bit mantissa, with the exact decoded value, hex, and special-case detection. Encode a decimal back to half too. Runs in your browser. It runs free in your browser on Gera Tools, with nothing uploaded.

IEEE-754 Float16 (Half) Inspector

Name: IEEE-754 Float16 (Half) Inspector
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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IEEE-754 half precision packs a floating-point number into just 16 bits, trading range and precision for compactness. It is the fp16 of machine learning and the half of GPU shaders. This inspector decodes every bit so you can see exactly what a half-float represents and encodes any decimal into its nearest half.

Bit layout

bit 15      bits 14..10        bits 9..0
sign (1)    exponent (5)       mantissa (10)

The exponent uses a bias of 15. For normal numbers (stored exponent 1–30):

value = (-1)^sign × 1.mantissa × 2^(stored_exponent − 15)

The implicit leading 1. is not stored. When the exponent is all zeros the number is subnormal: the implicit bit becomes 0 and the effective exponent is fixed at −14. An all-ones exponent with zero mantissa means infinity; non-zero mantissa means NaN.

Key limits of float16

Property	Value
Largest finite value	65504 (`0x7BFF`)
Smallest positive normal	2^−14 ≈ 0.0000610
Smallest positive subnormal	2^−24 ≈ 5.96 × 10^−8
Significant decimal digits	~3–4

Worked examples

Encoding 1.0: sign 0, true exponent 0 → stored 15, mantissa 0. Hex: 0x3C00. Decodes back to 1.0 exactly.

Encoding 65504: the largest finite half. Hex: 0x7BFF. The next representable value would need exponent field = 31, which means infinity.

Encoding 0.1: not exactly representable. The nearest half is 0x2E66, which decodes to approximately 0.0999756. The rounding error is about 0.024% — larger than in float32 or float64, which is why float16 is unsuitable for financial calculations.

Encoding 100000: overflow. This exceeds 65504, so the result is +Infinity (0x7C00). Float16’s limited range (versus bfloat16’s 10^38 range) is why the ML community sometimes prefers bfloat16 for training.

float16 vs bfloat16 — when to use which

Float16 has 10 mantissa bits (~3–4 decimal digits of precision) but only a 5-bit exponent (range ±65504). bfloat16 has only 7 mantissa bits (~2–3 digits of precision) but an 8-bit exponent matching float32’s full range (±3.4 × 10^38). In practice: float16 is common in graphics (GPU shaders, image data) where values fit in the ±65504 range; bfloat16 is preferred for deep-learning training where gradient magnitudes can be much larger.

Common uses of float16

GPU shaders: graphics APIs (Metal, Vulkan, WebGPU) natively support half for intermediate calculations where 3–4 digits of precision is enough and bandwidth is at a premium. Texture coordinates, color components (0–1 range), and lighting coefficients all fit well within float16’s range and precision.
Neural network inference: once a model is trained, its weights can be quantized to float16 for deployment with minimal accuracy loss, halving the memory footprint on edge hardware.
Scientific data compression: sensor readings with limited precision (e.g., temperature to 0.1°C, GPS altitude to 1 m) can often be stored in float16 rather than float32, reducing storage or transmission size by half.

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