Several different representations of real numbers have been proposed, but by far the most widely used is the floating-point representation. Floating-point representations have a base (which is always assumed to be even) and a precision p. If
= 10 and p
= 3, then the number 0.1 is represented as 1.00 × 10-1 . If = 2 and p = 24, then the decimal number 0.1 cannot be represented exactly, but is approximately 1.10011001100110011001101 × 2-4.
In general, a floating-point number will be represented as ± d.dd... d × e , where d.dd... d is called the significand and hasp digits. More precisely ±d0 . d1 d2 ... dp-1 × e represents the number .
The term floating-point number will be used to mean a real number that can be exactly represented in the format under discussion. Two other parameters associated with floating-point representations are the largest and smallest allowable exponents, emax and emin. Since there are p possible significands, and emax - emin + 1 possible exponents, a floating-point number can be encoded in
bits, where the final +1 is for the sign bit.