How is a real value stored in a computer?

Answer 1

Real (arbitrarily precise) values cannot be stored in a computer. They are generally approximated with either floating-point or fixed-point approximations.

A commonly used data type is "double-precision" which stores numbers accurately to about 16 decimal places, suitable for most real-world applications. More complex data structures known as "Bignum"s can be used to represent real numbers to arbitrary precision, depending on the amount of computer memory available. The programmer should always be aware that the computer cannot represent any real number.

If the computer has N bits of memory (including disk space), then it can be in one of 2^N possible states. No matter what N is, there are more real numbers between 0 and 1 than that. So a computer cannot possibly represent a continuum of real numbers between 0 and 1, let alone a wider range.

Source: See Related Links