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The IEEE 754 standard defines the format for representing floating-point numbers in computer systems. Here’s an overview of the IEEE 754 standard for floating-point numbers:


  • Sign bit: 1 bit, indicating the sign of the number (positive or negative).
  • Exponent: A fixed number of bits representing the exponent of the number, typically biased to allow for both positive and negative exponents.
  • Fraction (Significand or Mantissa): A fixed number of bits representing the significant digits of the number, including the fractional part.

Single Precision (32 bits):

  • Sign bit: 1 bit
  • Exponent: 8 bits
  • Fraction: 23 bits
  • Total: 32 bits

Double Precision (64 bits):

  • Sign bit: 1 bit
  • Exponent: 11 bits
  • Fraction: 52 bits
  • Total: 64 bits

Special Values:

  • Zero: Exponent and fraction bits are all zero.
  • Denormalized numbers: Exponent is all zeros, allowing for subnormal numbers with a reduced precision.
  • Infinity: Exponent is all ones, and the fraction is all zeros.
  • NaN (Not a Number): Exponent is all ones, and the fraction is non-zero. NaNs are used to represent undefined or invalid operations, such as the result of dividing zero by zero.


  • The leading bit of the significand is typically assumed to be 1 (implicit leading bit), except for denormalized numbers, where the leading bit is explicitly set to zero.


  • IEEE 754 specifies different rounding modes for arithmetic operations, including round to nearest, round towards zero, round towards positive infinity, and round towards negative infinity.


  • IEEE 754 ensures that floating-point arithmetic operations are correctly rounded to the nearest representable value within the specified precision.


  • The standard defines arithmetic operations (addition, subtraction, multiplication, division), comparison operations, and special functions (sqrt, log, exp, etc.) for floating-point numbers.

The IEEE 754 standard provides a widely accepted and standardized representation for floating-point numbers, ensuring interoperability and consistency across different computer architectures and programming languages. It is commonly implemented in hardware and software systems supporting floating-point arithmetic.