Alberto Poblacion
10/19/2008 7:11:00 PM
"Nathan Sokalski" <njsokalski@hotmail.com> wrote in message
news:OLzCxngMJHA.4536@TK2MSFTNGP03.phx.gbl...
>I know that Single and Double can only store values that can be stored as
>x/2^y, such as 0.5 and 0.125. But when they attempt to store values such as
>0.1 or 0.2 whose exact value cannot be stored, what algorithm do they use
>to determine what value to store? Thanks.
They use a mantissa and an exponent, so that a number is expressed as
(mantissa)*10^(exponent). We do this frequently in everyday engineering work
when we say for instance, that something took "1.23*10^-6 seconds". However,
when speaking about Single and Double, the "10" has to be interpreted in
base 2 (meaning that it is a "2" in base 10). The exponent and mantissa are
also in base 2. The precission of the mantissa is limited, because the
mantissa and exponent and their signs have to fit into 4 bytes (Single) or 8
bytes (Double). The numbers that can be represented exactly are those that
can be converted into base 2 within that number of bits. For instance, 0.5
(base10) is 0.1 (base 2), but some numbers that have a small number of
decimals in base 10 have an infinite number of decimal places once converted
to base 2, so they will be truncated when assigned to the mantissa, and
therefore they will not be "exact".