Understand how decimal numbers are represented in binary floating-point format using the IEEE 754 standard. This calculator converts your input into its sign, exponent, and mantissa components, illustrating both single (32-bit) and double (64-bit) precision. Essential for computer science students, engineers, and developers exploring data representation and numerical accuracy.
Formula:
The IEEE 754 floating-point standard represents a number (N) in the form:
N = (-1)S × (1 + M) × 2(E - Bias)
- S: The Sign bit (0 for positive, 1 for negative).
- M: The Mantissa (or Fraction), representing the significant digits.
- E: The Exponent, adjusted by a fixed Bias.
Bias is 127 for Single Precision (32-bit) and 1023 for Double Precision (64-bit).