utils logo UTILS
Free online tools to generate, calculate,
convert, format, encode, and play.
 

IEEE 754 Floating Point Converter

Convert between decimal numbers and their IEEE 754 binary floating point representation. View sign, exponent, and mantissa bit fields for single (32-bit) and double (64-bit) precision.

Decimal to IEEE 754

Examples:

Hex / Binary to IEEE 754

How It Works

The IEEE 754 standard defines how floating point numbers are stored in binary. A number is split into three fields: sign, exponent, and mantissa (also called the significand).

Single Precision (32-bit)

  • Sign: 1 bit (0 = positive, 1 = negative)
  • Exponent: 8 bits (bias = 127)
  • Mantissa: 23 bits (+ 1 implicit bit)
  • Range: ~1.2 × 10-38 to ~3.4 × 1038
  • Precision: ~7 decimal digits

Double Precision (64-bit)

  • Sign: 1 bit (0 = positive, 1 = negative)
  • Exponent: 11 bits (bias = 1023)
  • Mantissa: 52 bits (+ 1 implicit bit)
  • Range: ~2.2 × 10-308 to ~1.8 × 10308
  • Precision: ~15–17 decimal digits

The value is computed as:

value = (-1)sign × 2(exponent - bias) × (1 + mantissa)

Special Values

ValueExponentMantissaMeaning
+0 / -0All 0sAll 0sPositive/Negative zero
DenormalizedAll 0sNon-zeroVery small numbers (no implicit 1)
±InfinityAll 1sAll 0sOverflow / division by zero
NaNAll 1sNon-zeroNot a Number (0/0, sqrt(-1))

Common Use Cases

Debugging

  • Understanding floating point rounding errors
  • Inspecting float bit patterns in memory dumps
  • Verifying serialization/deserialization
  • Diagnosing precision loss in calculations

Education

  • Learning binary number representation
  • Computer architecture coursework
  • Understanding why 0.1 + 0.2 ≠ 0.3
  • Exploring denormalized numbers and special values

Related Utils

Bin/Dec/Hex/Oct Converter Scientific Notation Number Base Converter ASCII/Unicode Converter

Feedback

Help us improve this page by providing feedback, and include your name/email if you want us to reach back. Thank you in advance.


Share with