Floating-Point Notation Definition/Meaning:
A representation of real numbers that enables both very
small and very large numbers to be conveniently expressed. A floating-point
number has the general form
± m x Re
where m is called the mantissa, R is the radix (or base) of the number system,
and e is the exponent.
The following format is typical of the floating-point
representation used in computers. The first bit is a sign bit, denoting the sign
of the mantissa. This is followed by a fixed number of bits representing the
exponent, which is in turn followed by another fixed number of bits representing
the magnitude of the mantissa. The exponent is often represented using excess-n
notation, whereby a number, called the characteristic (or biased exponent), is
stored instead of the exponent itself. To derive the characteristic for a
floatingpoint number from its exponent, the bias (or excess factor) n is added
to the exponent. For example, for an 8-bit characteristic, exponents in the
range -128 to + 127 are represented in excess -128 notation by characteristics in
the range 0 to 255.
A nonzero floating-point number is normalized if the leading digit in its
mantissa is nonzero.