Floating-point

floating-point

   <programming, mathematics> A number representation consisting
   of a {mantissa}, M, an {exponent}, E, and a {radix} (or
   "base").  The number represented is M*R^E where R is the
   radix.

   In science and engineering, {exponential notation} or
   {scientific notation} uses a radix of ten so, for example, the
   number 93,000,000 might be written 9.3 x 10^7 (where ^7 is
   superscript 7).

   In computer hardware, floating point numbers are usually
   represented with a radix of two since the mantissa and
   exponent are stored in binary, though many different
   representations could be used.  The {IEEE} specify a
   {standard} representation which is used by many hardware
   floating-point systems.  Non-zero numbers are {normalised} so
   that the {binary point} is immediately before the most
   significant bit of the mantissa.  Since the number is
   non-zero, this bit must be a one so it need not be stored.  A
   fixed "bias" is added to the exponent so that positive and
   negative exponents can be represented without a sign bit.
   Finally, extreme values of exponent (all zeros and all ones)
   are used to represent special numbers like zero and positive
   and negative {infinity}.

   In programming languages with {explicit typing},
   floating-point types are introduced with the keyword "float"
   or sometimes "double" for a higher precision type.

   See also {floating-point accelerator}, {floating-point unit}.

   Opposite: {fixed-point}.

   (2008-06-13)