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Interactive 3D/Floating Point Arithmetic
Float Type
Total bits:32
Sign:1 bit
Exponent:8 bits
Mantissa:23 bits
Value Slider
value ≈ 3.1400
Special Values
IEEE 754: value = (-1)^s × 2^(e-bias) × 1.mantissa
Colored bits light up for 1s. Hover over sections to see sign (red), exponent (amber), mantissa (indigo).
Precision loss: float32 has ~7 decimal digits. Numbers like 1e7+1 round to 1e7 - the +1 disappears entirely. This causes silent bugs in ML training.

Floating Point Arithmetic - Interactive Visualization

IEEE 754 floating point represents real numbers as sign × mantissa × 2^exponent. Float32 uses 1 sign bit, 8 exponent bits, 23 mantissa bits - giving about 7 decimal digits of precision. This precision limitation causes subtle ML bugs: gradient vanishing/explosion, catastrophic cancellation, and training instability in float16. This visualization shows all 32 bits for any value.

  • See all 32 bits of float32 light up for any value you enter
  • Watch precision loss: (x + 1) - x ≠ 1 for large x
  • See special values: +Inf, -Inf, NaN, denormals, -0
  • Compare float16, float32, float64 precision and range
  • Foundation for mixed-precision training, loss scaling, and numerical debugging

Part of the EngineersOfAI Interactive 3D - free interactive visualizations covering every major concept in machine learning and AI engineering. Hover any element for a plain-English explanation. No code required.