Number Representations & States

"how numbers are stored in computers""how numbers are stored in computers"

Machine Epsilon

Every floating-point format has a worst-case relative error for a single rounding operation. This is often called machine epsilon and represented in the theorems as .

In round-to-nearest mode, , where is the unit in the last place for the number 1. For IEEE 754 double precision, , which implies that a correctly rounded floating-point number differs from by at most about 1 part in for a well-behaved computation.