Question

1. The cardinality of a set is the number of elements it contains. Under IEEE floating point representation, what is the cardinality of the floats?

Answer 1

IEEE Floating Point Representation :

• The Institute of Electrical and Electronic Engineers (IEEE) set a technical standard regarding rounding of floating point numbers, i.e., rounding of decimal numbers which have to satisfy a set of rules during mathematical conversions.

Cardinality :

• Cardinality is a concept of determining the size of number sets.
• For finite number sets, the cardinality is equal to the size of the finite set.
• For an infinite set, like, floating point number set where the number of bits is not specified, it can extend to negative or positive limits of infinity, depending on the number of decimal places that the numbers in the set can extend to. If the number of bits of the floating point number are specified to be "n", the cardinality of float can roughly be estimated to 2^n, where 'n' is the number of bits specified.