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.

IEEE-754 Float16 (Half) Inspector

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.

How it works

The 16 bits split into three fields:

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

The exponent uses a bias of 15. For a normal number (stored exponent 1 to 30) the value is:

value = (-1)^sign x 1.mantissa(binary) x 2^(exponent - 15)

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

Notes and examples

The largest finite half is 0x7BFF, which equals 65504. The smallest positive normal is 2^-14, and subnormals reach down to 2^-24. Precision is about 3 to 4 significant decimal digits. Because the mantissa is only 10 bits, encoding a decimal like 0.1 to half and back will not be exact, which the encode direction of this tool makes visible by showing the nearest representable value.