Number Representations & States

"how numbers are stored and used in computers""how numbers are stored and used in computers"

IEEE754

In the IEEE 754 standard for floating-point arithmetic, a real number is approximated using a format like:

Where:

• : Sign bit
• : Mantissa or significand (typically normalized)
• : Exponent

Because only a finite number of bits are used to store and , not every real number can be exactly represented — hence the need to analyze errors introduced in representation and computation.