🔬 IEEE 754 Float Converter

🔄 Conversion Mode

🎯 Precision

Single precision: 1 sign + 8 exponent + 23 mantissa bits

Double precision: 1 sign + 11 exponent + 52 mantissa bits

📝 Input Format

📝 {{ getInputLabel() }}

Precision: {{ precision ==='single' ?'32-bit float' :'64-bit double' }} Format: {{ inputFormat ==='binary' ?'Binary string' :'Hexadecimal' }}

💡 Quick Examples

📤 {{ getOutputLabel() }}

🔍 IEEE 754 Bit Breakdown

Bit Layout:

Sign | Exponent | Mantissa/Fraction

Sign Bit: {{ bitBreakdown.signBit }} ({{ bitBreakdown.signBit ==='0' ?'Positive' :'Negative' }})

Exponent: {{ bitBreakdown.exponentBits }}

Binary: {{ bitBreakdown.exponentDecimal }}, Biased: {{ bitBreakdown.exponentBiased }}, Actual: {{ bitBreakdown.exponentActual }}

Mantissa: {{ bitBreakdown.mantissaBits }}

Decimal value: {{ bitBreakdown.mantissaDecimal }}

Special Case: {{ bitBreakdown.specialCase }}

📖 IEEE 754 Reference

Single Precision (32-bit):

1 sign bit
8 exponent bits
23 mantissa bits
Bias: 127

Double Precision (64-bit):

1 sign bit
11 exponent bits
52 mantissa bits
Bias: 1023

Special Values:

Zero: Exponent = 0, Mantissa = 0
Infinity: Exponent = all 1s, Mantissa = 0
NaN: Exponent = all 1s, Mantissa ≠ 0
Denormalized: Exponent = 0, Mantissa ≠ 0

⚠️ {{ error }}

ℹ️ About IEEE 754 Float Converter

IEEE 754 floating point is the binary number format used by CPUs, programming languages, file formats, debuggers, and network protocols to store non-integer values. The IEEE 754-2019 standard defines interchange formats, arithmetic behavior, exceptions, signed zero, infinities, subnormal values, and NaN values. This converter focuses on the two common binary interchange formats: binary32 single precision and binary64 double precision.

What the bits mean: an IEEE 754 binary value is split into a sign bit, a biased exponent, and a fraction/significand field. Single precision uses 1 sign bit, 8 exponent bits, and 23 fraction bits; double precision uses 1 sign bit, 11 exponent bits, and 52 fraction bits. The exponent field controls scale, while the fraction field stores the significant binary digits. All-zero and all-one exponent fields are reserved for zeros, subnormal numbers, infinities, and NaN encodings.

Decimal to IEEE 754: enter a decimal value such as 1.0, 3.14159, 0.1, -0, or Infinity to inspect the binary and hexadecimal encoding.
IEEE 754 to decimal: paste a 32-bit or 64-bit binary string, or a hexadecimal word such as 40490FDB, to decode the stored value.
Bit-field analysis: read the sign, exponent, and mantissa/fraction fields separately when debugging binary packets, firmware dumps, save files, or serialization formats.

Practical examples: binary32 1.0 is 3F800000, binary32 -1.0 is BF800000, and binary64 1.0 is 3FF0000000000000. The single-precision hex value 40490FDB decodes to approximately 3.1415927410125732, while the double-precision hex value 400921FB54442D18 decodes to 3.141592653589793. Comparing those two pi encodings is a quick way to see how precision changes the stored value.

When this tool helps:

Explaining why values such as 0.1 cannot always be represented exactly in base-2 floating point.
Checking float and double constants used in C, C++, Java, JavaScript, Python, Rust, Go, and shader code.
Reverse engineering binary file formats, telemetry payloads, game saves, PLC data, or protocol fields that store floats.
Verifying endian-normalized hexadecimal values before copying them into tests, parsers, packet dissectors, or documentation.

Limitations: decimal input is parsed by the browser as a JavaScript number before it is packed into binary32 or binary64, so very long decimal strings and custom rounding modes are outside this page's scope. Hex and binary inputs are treated as normalized IEEE 754 bit patterns, not as little-endian memory dumps. The converter can identify NaN and infinity encodings, but it is not a full floating-point arithmetic simulator and does not preserve every implementation-specific NaN payload behavior.

API Usage Example:

POST /api/tools/conversion/ieee754-float
Content-Type: application/json

{
    "input": "3.14159",
    "mode": "decimal-to-ieee754",
    "precision": "single",
    "inputFormat": "binary"
}