IEEE 754 Calculator
Convert floating-point numbers (float/double) to binary representation. View the Sign, Exponent, and Mantissa bits clearly for single and double precision numbers.
Sign (1)
Exponent (8)
Mantissa (23)
0
10000000
10010010000111111010000
How IEEE 754 works for 3.14159
Sign Bit
0 indicates a positive number.
Exponent
Binary: 10000000
Decimal: 128
Actual: 1 (Bias 127)
Mantissa (Fraction)
Binary: 10010010000111111010000
Represents the precision bits. The leading 1 is implicit.
What is IEEE 754?
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) defines how computers store fractional numbers. Use this float to binary calculator to inspect the exact Sign, Exponent, and Mantissa bits for single precision (32-bit) and double precision (64-bit).
Parts of a Float:
- Sign Bit: 1 bit determining if the number is positive (0) or negative (1).
- Exponent: Determines the magnitude of the number, using a bias (127 for single, 1023 for double).
- Mantissa (Fraction): The precision bits representing the significant digits.