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IEEE 754 Floating-Point Visualizer
Interactive visualization of 32-bit Single Precision and 64-bit Double Precision floating-point numbers.
IEEE 754 is the technical standard for floating-point computation established by the IEEE in 1985.
Layout Specifications:
- Single Precision (32-bit): 1 sign bit [31], 8 exponent bits [30-23] (bias = 127), 23 fraction bits [22-0].
- Double Precision (64-bit): 1 sign bit [63], 11 exponent bits [62-52] (bias = 1023), 52 fraction bits [51-0].
Special Cases:
- Zero: Exponent = 0, Fraction = 0
- Denormalized (Subnormal): Exponent = 0, Fraction ≠ 0. Value is (-1)S × 0.F × 21-bias.
- Infinity: Exponent = All 1s (255 or 2047), Fraction = 0
- NaN (Not a Number): Exponent = All 1s, Fraction ≠ 0
When you need it: Debugging why a float comparison fails, reading a float out of a raw memory dump, or understanding precision loss when porting math to a 32-bit MCU.
Worked example: 0.1f is stored as 0x3DCCCCCD ≈ 0.100000001 — not exact, which is exactly why 0.1 + 0.2 ≠ 0.3. A float32 is 1 sign bit, 8 exponent bits (bias 127), and 23 mantissa bits.
Tips & gotchas:
- Never compare floats with
==; test|a − b| < epsiloninstead. NaNis never equal to anything, including itself — use it to detect it (x != x).- float32 carries ~7 significant decimal digits, float64 ~15; pick the width your dynamic range needs.
- Watch byte order when reading floats from a dump — the four bytes are stored little-endian on most MCUs.