IEEE 754 Float Converter
IEEE 754 standard floating-point (Float/Double) hexadecimal representation and binary bit structure analysis.
Binary Representation
| Sign | Exponent | Mantissa |
|---|---|---|
| 0 | ||
| + | Value: 0 (Raw: 0) | 1.... |
Formula: (-1)0 × 20 × (1 + 0.)
Usage
Standard Overview
IEEE 754 is the most widely used binary floating-point arithmetic standard, defining how floating-point numbers are stored in computers. Single precision (Float 32-bit): 1 sign bit, 8 exponent bits, 23 mantissa bits, bias 127; Double precision (Double 64-bit): 1 sign bit, 11 exponent bits, 52 mantissa bits, bias 1023. JavaScript's Number type uses double precision by default.
Bit Structure
Sign bit (red): 0 for positive, 1 for negative; Exponent bits (green): stores actual exponent plus bias, enabling representation of positive and negative exponents; Mantissa bits (blue): stores the fractional part; the implicit leading 1 is not stored (for normalized numbers). Formula: (-1)^sign × 2^(exponent-bias) × (1 + mantissa).
Steps
1. Use the top tabs to switch between single and double precision modes; 2. Enter a value in the "Decimal Float" box to auto-calculate Hex and bit structure; 3. You can also enter a Hex value in the "Hexadecimal" box to parse in reverse; 4. View the binary bit structure (sign/exponent/mantissa shown in different colors); 5. Refer to the formula to understand the conversion process.
Notes
Special values: all-zero exponent means denormalized number or zero; all-one exponent means infinity or NaN; this tool does not support Decimal Float format; Hex input shorter than required is auto-padded with 0s, longer input is truncated; switching modes triggers auto-recalculation of current input.