A decimal number is a number that uses a base 10 system, with digits ranging from 0 to 9, to represent a value or quantity.
A floating-point representation is a method of representing numbers with decimal points in a computer system. It uses a combination of a sign, a base, a significand (or mantissa), and an exponent to represent a wide range of values with varying precision.
To convert a decimal number to floating-point representation, the number is first normalized so that it is in the form of a number between 1 and 10, multiplied by a power of 10. The normalized number is then represented in binary form, followed by the binary representation of the exponent.
The main difference between single-precision and double-precision floating-point representation is the number of bits used to represent the significand or mantissa. Single-precision uses 32 bits, while double-precision uses 64 bits. This means that double-precision can represent a larger range of values with higher precision compared to single-precision.
One potential error that can occur is rounding errors, which can result in a loss of precision. Another error is overflow, which happens when the number being converted is too large to be represented in the given number of bits. Underflow is also a possible error, occurring when the number is too small to be represented.