What is a NaN and what is its significance in floating?point arithmetic?

What will be an ideal response?

The IEEE 754 floating?point standard represents real numbers and three special entities: plus infinity, minus infinity, and not a number, NaN. The NaN cannot be interpreted as a normal floating?point value. That is, a NaN is a value that is outside the IEEE 754 standard. This mechanism allows the designer to use the bits of a floatingpoint value to represent anything that he or she wishes; it’s a form of escape code. The NaN has the curious property that it is unordered and is not larger or smaller than another number including itself! A NaN is represented by an all 1s exponent and a non?zero mantissa.

Some literature divides NaNs into two categories: quiet NaNs that can be propagated in computer arithmetic, and signalling NaNs that can be used to force an exception.