You can also verify that taking the two??™s
complement of ??’6 correctly represents +6.
Larger word sizes work the same way; there are simply more bits with which to represent the magnitude
of the number. These representations are called ???integer??? or ???integral??? number representations. They provide
a means of representing whole numbers for computation.
REAL NUMBER FORMATS
Numbers containing fractions are more difficult to represent. Real numbers consist of a mantissa and
an exponent. Computer designers decide how to allocate the bits of the computer word so that some can be
used for the mantissa and some for the exponent. In addition, the mantissa can be positive or negative, and the
exponent can be positive or negative.
You might imagine that different designers could create different definitions for real number formats.
A larger mantissa will provide greater precision; a larger exponent will provide for larger and smaller magnitudes
(scale). As recently as the 1980s, different computer manufacturers used different representations, and those
differences made it difficult to move data between computers, and difficult to move (???port???) programs from one
make of computer to another.
Since then, the IEEE has created a standard for binary floating-point number representation using 32 and
64 bits.
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