IEEE 754 float32 values in [0, 1] – live WebGPU

Every glowing dot is a real single-precision float generated with the exact hardware formula:

value = (1 + mantissa) × 2exponent
exponent runs from –126 to 0  |  mantissa is a fraction in [0, 1)

Linear scale = true number line → almost all values sit extremely close to zero (the bright bar).
Log scale = position ∝ log₁₀(value) → shows that floats exist at every order of magnitude from ~10⁻³⁸ up to 1.

WebGPU: instance buffer holds every float + phase. Vertex shader maps value → screen X (linear/log) + bobbing. Fragment shader makes soft circles. Additive blending shows density.

Current: Log scale
WebGPU ready · 0 / 0 points
0
1
10⁻³⁰
10⁻²⁰
10⁻¹⁰
10⁻⁵
0.01
0.1

Scientific Notation & Computing

In scientific notation a number is written as a significand (also called the mantissa) multiplied by a power of ten (or two in binary).

Example: 5.3266 × 10³
→ The part 5.3266 is the significand (mantissa).
→ The part 10³ is the exponent that scales the value.

Value scaling: The significand carries the precision (the significant digits), while the exponent controls the magnitude (how large or small the number is). Together they let computers represent both very large and very tiny numbers with a fixed number of bits.

In IEEE 754 binary floating-point the significand is stored in normalized form (usually with a leading 1 that is implicit). That is exactly why the formula you see in the visualization is written as (1 + mantissa) × 2exponent.

Color Meaning

Cyan / blue points (left side) = very small floating-point numbers (close to 0).

Pink / magenta points (right side) = floating-point numbers that are relatively close to 1.0 (for example 0.5, 0.75, 0.9, 0.99, etc.).

In Linear scale you see very few pink points because almost all possible float32 values are packed tightly near zero.
In Log scale the pink points become more visible because the scale spreads out the larger magnitudes.

Want to go deeper? I can next show you exactly how the mantissa is stored in the 23 bits of a float32, or walk through extracting a logarithmic mantissa step-by-step.