IEEE 754 Floating Point Converter

Break a decimal number into 32-bit and 64-bit IEEE 754, and decode hex/binary bit patterns back into numbers.

Category: Converters

When to use?

Use it to learn how floating point is stored, or to decode float bit patterns in embedded/low-level debugging. It breaks numbers into sign, exponent and mantissa, and shows why values like 0.1 aren’t stored exactly.

How to use

  • On the "Decimal → IEEE 754" tab, enter a number to see the 32- and 64-bit breakdown.
  • Or on the "Hex/Binary → Decimal" tab, enter a bit pattern and precision.
  • Inspect and copy the sign/exponent/mantissa bits, hex, and stored value.

Input Explanation

Enter a decimal number (e.g. 0.1, -3.14, 1e10, Infinity) or an IEEE 754 bit pattern (8/16 hex digits or 32/64 binary digits).

Calculation Basis

Bits are extracted with ArrayBuffer/DataView setFloat32/setFloat64 and split into sign, exponent and mantissa. Decoding reads the pattern back as a float to show the stored value.

Usage Examples

  • Learning floating point - See the sign/exponent/mantissa structure and rounding error directly.
  • Low-level debugging - Decode float bit patterns (hex) from memory dumps into real numbers.

Examples

  • 0.1 → 32-bit 0x3DCCCCCD, stored value 0.10000000149011612
  • 0x3FB999999999999A (64-bit) → 0.1

Cautions

  • 32-bit single precision has limited accuracy, so the stored value may differ from your input (rounding).
  • Bytes are interpreted in big-endian order.

FAQ

Why isn’t 0.1 stored exactly?

0.1 has no finite binary fraction, so it is rounded to the nearest representable value.

Single vs double precision?

Single (32-bit) uses 8 exponent + 23 mantissa bits; double (64-bit) uses 11 + 52 bits for more precision.

Can I decode from hex?

Yes — enter a hex or binary bit pattern with the precision to decode the original number.

Related Tools

  • Number Base Converter - Convert between binary, octal, decimal, and hexadecimal.
  • Unit Converter - Freely convert units of length, weight, temperature, area, and volume.
  • Hash Generator - Convert text into SHA-1, SHA-256, and SHA-512 hashes.
  • URL Encode / Decode - Encode text into URL-safe form (%XX) or decode an encoded URL back to text.
  • Base64 Converter - Encode text to Base64 or decode a Base64 string back to text.
  • HTML Escape / Unescape - Convert HTML special characters to entities, and restore entity strings back to characters.