Supports IEEE 754 single and double precision floating point conversion. Convert decimal numbers to binary representation, or vice versa. Completely free, no registration required.
Start ConversionSupports conversion from decimal to floating point and vice versa.
Supports IEEE 754 single precision (32-bit) and double precision (64-bit) floating point formats.
Provides detailed breakdown of floating point structure including sign, exponent, and mantissa bits.
IEEE 754 is the standard for representing floating-point numbers in computers, defining the format, rounding rules, exception handling, and more.
The value of a floating-point number is calculated as: (-1)sign × (1 + mantissa) × 2(exponent - bias)
Where the bias is 127 for single precision and 1023 for double precision.
IEEE 754 is a technical standard established by the Institute of Electrical and Electronics Engineers for floating-point arithmetic. It is widely used in computer systems to represent real numbers, defining the format, rounding rules, exception handling, and ensuring consistency in floating-point operations across different computer systems.
Single precision floating point uses 32 bits of storage: 1 sign bit, 8 exponent bits, and 23 mantissa bits, providing approximately 6-7 decimal digits of precision. Double precision uses 64 bits: 1 sign bit, 11 exponent bits, and 52 mantissa bits, providing approximately 15-16 decimal digits of precision. Double precision has a larger range and higher precision than single precision.
Since floating-point numbers use a finite number of binary bits to represent real numbers, and many decimal fractions cannot be exactly represented as binary fractions, rounding errors occur. Additionally, floating-point numbers have a limited range, and values outside this range cause overflow or underflow. These factors can lead to precision errors in floating-point calculations.
Our tool supports special values defined by the IEEE 754 standard, including positive zero, negative zero, positive infinity, negative infinity, and NaN (Not a Number). These special values are used in floating-point calculations to represent specific mathematical concepts or error conditions.