Float Input
浮点数转换结果
32位 IEEE 754 单精度
64位 IEEE 754 双精度
Usage Guide
- Select floating-point precision (single precision 32-bit or double precision 64-bit)
- Method 1: Enter floating-point number to view its binary representation
- Method 2: Enter binary code to convert to floating-point number
- View detailed bit field breakdown (sign bit, exponent bits, mantissa bits)
- Copy conversion results to clipboard
IEEE 754 Standard Knowledge
IEEE 754 Standard Introduction
IEEE 754 is a floating-point arithmetic standard that defines floating-point formats, operation rules, exception handling, etc. This standard is widely used in computer systems, ensuring consistency of floating-point operations across different systems.
Single Precision Float (32-bit)
Single precision floating-point uses 32 bits: 1 sign bit, 8 exponent bits (biased by 127), 23 mantissa bits. Value range is approximately ±1.18×10⁻³⁸ to ±3.40×10³⁸, with precision of about 7 decimal digits.
Double Precision Float (64-bit)
Double precision floating-point uses 64 bits: 1 sign bit, 11 exponent bits (biased by 1023), 52 mantissa bits. Value range is approximately ±2.23×10⁻³⁰⁸ to ±1.80×10³⁰⁸, with precision of about 15-16 decimal digits.
Special Values
IEEE 754 defines special values: positive and negative zero, positive and negative infinity, NaN (Not a Number). These special values handle special cases like division by zero, overflow, undefined operations.
Application Scenarios
In programming debugging, numerical computation, embedded development, graphics processing, understanding binary representation of floating-point numbers is crucial for analyzing precision issues and optimizing algorithm performance.