IEEE 754 Floating Point Converter

Summary

Enter a decimal number to see its IEEE 754 single (32-bit) and double (64-bit) floating-point binary breakdown with sign, exponent, and mantissa fields.

How it works

1. Enter any decimal number in the input field (e.g. 3.14, -0.5, 1e10).
2. The tool extracts the sign bit (0 = positive, 1 = negative).
3. It calculates the biased exponent by adding 127 (single) or 1023 (double) to the actual exponent.
4. The mantissa (significand) stores the fractional part of the normalized binary value.
5. Results are shown as color-coded binary strings and hexadecimal encoding.
6. Special values like Infinity, NaN, and zero are handled and labeled automatically.

Use cases

• Debug floating-point precision issues in C, C++, Java, or embedded code.
• Learn how IEEE 754 represents real numbers at the bit level.
• Verify float/double encodings when working with binary file formats or network protocols.
• Understand why 0.1 + 0.2 != 0.3 by inspecting the actual bit patterns.
• Check NaN, Infinity, and subnormal number representations.
• Reverse-engineer hex dumps containing floating-point data.

Frequently Asked Questions