More on Computer Arithmetic
Computers usually assume implicitly that the most significant bit of the mantissa is 1 and hence increase the size of the mantissa. Thus, the normalised representation of fl oating point numbers is
Single Precision.
Numbers stored using 4 bytes, i.e. 32 bits, with a 1-bit sign indicator, an 8-bit exponen
and a 23-bit mantissa are called single precision oating point. (Here,
)
The absolute value of the largest and smallest single precision floating point numbers are,
and
respectively. The machine error is
Hence calculations are correct to 7 decimal places (i.e. numbers have 7 significant digits).
Note that, n = 0 and n = 255 are used to represent special values (zero, infinity).
Double precision
Numbers stored using 8 bytes, i.e. 64 bits, with a 1-bit sign indicator, an 11-bit exponent,
and a 52-bit mantissa, are called double precision floating point. (Here,
)
The absolute value of largest and smallest double precision floating point numbers are,
and
respectively.
The machine error
Hence calculations are correct to 16 decimal
places (i.e. numbers have 16 significant digits).
Again,
and
are used to represent special values.