IEEE 754 Floating-Point Converter
Convert decimal numbers to IEEE 754 binary representation
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Sign
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Exponent
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Mantissa
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How IEEE 754 Works
IEEE 754 is a technical standard for floating-point arithmetic established by the Institute of Electrical and Electronics Engineers (IEEE). It defines how computers represent and manipulate decimal numbers in binary format.
Structure
IEEE 754 floating-point numbers are divided into three parts:
Sign Bit
1 bit determining if the number is positive (0) or negative (1)
Exponent
8 bits (single) or 11 bits (double) for the power of 2, using biased representation
Mantissa (Fraction)
23 bits (single) or 52 bits (double) for the significant digits
Formula
Value = (-1)sign × 2(exponent - bias) × (1 + mantissa)
- Bias: 127 for single precision (32-bit), 1023 for double precision (64-bit)
- Single Precision: 1 sign bit + 8 exponent bits + 23 mantissa bits = 32 bits
- Double Precision: 1 sign bit + 11 exponent bits + 52 mantissa bits = 64 bits
- Range: Single precision: ±1.18×10-38 to ±3.4×1038
- Precision: Single: ~7 decimal digits, Double: ~15-16 decimal digits
Special Values
- Zero: All exponent and mantissa bits are 0
- Infinity: All exponent bits are 1, all mantissa bits are 0
- NaN (Not a Number): All exponent bits are 1, mantissa is non-zero