What types of numbers are representable in binary floating-point?

Question

I\'ve read a lot about floats, but it\'s all unnecessarily involved. I think I\'ve got it pretty much understood, but there\'s just one thing I\'d like to know for

Answer 1

Floating-point numbers are literally represented using the form:

1.m * 2^e

Where 1.m is a binary fraction and e is a positive or negative integer.

As such, you can represent 1/32 + 1/16 exactly, as:

1.1000000 * 2^-4

(1.10 being the binary fraction equivalent to 1.5.) 1/48, however, is not representable in this format.