Q. Explain about Floating Point Numbers?

The IEEE Standard 754 floating point is the most common representation today for real numbers on computers.

There are numerous ways to represent real numbers on computers. The Fixed point places a radix point somewhere in the middle of the digits, and is equivalent to using integers that represent portions of some unit.

For illustration, one might represent 1/100ths of a unit; if you have four decimal digits, you could represent 10.82, or 00.01. One more approach is to use rationals, and represent every number as the ratio of two integers.

The Floating-point representation - the most common solution - basically represents reals in scientific notation. The Scientific notation represents numbers as a base number and an exponent. For illustration, 123.456 could be represented as 1.23456 × 102. In the hexadecimal, the number 123.abc might be represented as 1.23abc × 162.

The Floating-point solves a number of representation problems. A Fixed-point has a fixed window of representation, which limits it from representing very large or very small numbers. As well, fixed-point is prone to a loss of precision when two large numbers are divided.

The Floating-point, on the other hand, employs a sort of "sliding window" of precision appropriate to the scale of the number. This permits it to represent numbers from 1,000,000,000,000 to 0.0000000000000001 with ease.