IEEE-754 Floating-Point Converter

Convert decimal values to IEEE-754 binary32 and binary64, or decode a bit pattern or hexadecimal value. Inspect each field, classification, and the exact value represented by the bits.

Use it to explore floating-point precision, rounding, normal and subnormal numbers, and special values.

Conversion direction

Enter a decimal number, scientific notation, Infinity, -Infinity, or NaN.

What this tool does

IEEE-754 defines how common binary floating-point formats store a sign, an exponent, and a fraction. This converter shows those fields for 32-bit single precision and 64-bit double precision values.

How to use the tool

  1. Choose Decimal to IEEE-754 and enter a decimal value to see both formats.
  2. Choose IEEE-754 to decimal, select the bit width and binary or hexadecimal input, then enter the full representation.
  3. Copy the uninterrupted bit pattern or hexadecimal value. Expand the exact decimal value when you need to inspect its full expansion.

Useful applications

  • Compare how binary32 and binary64 round the same decimal input.
  • Read floating-point values from binary or hexadecimal data and identify zeros, subnormals, infinities, and NaNs.

Notes and limitations

  • The fraction field stores only the trailing fraction bits. Normal numbers have an implicit leading 1 in their significand; subnormal numbers do not and use an exponent of 1 minus the bias.
  • The exponent field is stored with a bias: 127 for binary32 and 1023 for binary64. Many base-10 fractions, including 0.1, have no finite binary expansion, so the stored value is rounded.
  • Binary32 has 23 stored fraction bits and binary64 has 52, giving binary64 more precision and a wider range. The exact decimal expansion is available in each finite result.
  • Infinity represents an unbounded result. NaN marks a result that is not a number. Different NaN bit patterns remain visible in reverse conversion; this tool does not assign meaning to their payload bits.

Frequently asked questions

Why can the represented value differ from the decimal input?

A decimal fraction may not have a finite binary expansion. The format stores the nearest representable value, which the exact decimal expansion makes visible.

What does the exponent bias do?

The bias lets an unsigned exponent field encode both negative and positive exponents. Subnormal values use 1 minus the bias as their scaling exponent.

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