## 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 exponenand 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,

andrespectively. The machine error isHence 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,andrespectively.

The machine errorHence calculations are correct to 16 decimal

places (i.e. numbers have 16 significant digits).

Again,andare used to represent special values.