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 http://docs.sun.com/source/806-3568/chars/beta.gif (which is always assumed to be even) and a precision p. If http://docs.sun.com/source/806-3568/chars/beta.gif
= 10 and p
= 3, then the number 0.1 is represented as 1.00 × 10-1 . If http://docs.sun.com/source/806-3568/chars/beta.gif = 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 × http://docs.sun.com/source/806-3568/chars/beta.gife , where d.dd... d is called the significand and hasp digits. More precisely ±d0 . d1 d2 ... dp-1 × http://docs.sun.com/source/806-3568/chars/beta.gife represents the number http://docs.sun.com/source/806-3568/...oldberg283.gif .
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 http://docs.sun.com/source/806-3568/chars/beta.gifp possible significands, and emax - emin + 1 possible exponents, a floating-point number can be encoded in
http://docs.sun.com/source/806-3568/...oldberg278.gif bits, where the final +1 is for the sign bit.