(all numbers discussed are in decimal)
lets say we have a floating point data type that is like :
m * 10 ^ e
where m is the mantissa . and max mantissa size is 1 ( 0 <= m <= 9); e is the exponent and its size is -1 <= e <= 1
we say our data type Max value is 90 and its Min value is 0
BUT : that does not mean we can represent all numbers that are in this limit . we can only represent 27 numbers ( 9 * 3 ) excluding zero.
specifically we can't represent 89 in this way since it has a two digit mantissa (and non of them are zero).
so technically analogous to the above descriptions . in a float data type (in any programming language) there must be some integers between Max and Min values that we cannot store in a float data type .
is the above argument sound . if it is please give an example how to show this in java or c ?