How many numbers can a 32 bit float represent

Question

Using the IEEE Standard for float, how many different numbers can a 32 bit float represent?

Lorelle

Answer 1

Each bit pattern in an IEEE-754 binary32 format represents a distinct number except:

• Zero is represented twice, as +0 and −0. Thus, one is a duplicate.
• Patterns with all ones in the eight-bit exponent field and a non-zero value in the 23-bit primary significand field represent a Not-a-Number (NaN). The number of these is 2•(2²³−1). (The initial factor of two is for the sign bit.)

There are 2³² bit patterns. Subtracting the duplicate and the NaNs gives 2³² − 1 − 2•(2²³−1) = 4,278,190,081.

Note that the above includes +∞ and −∞. To limit it to finite numbers, subtract two.

Nikolai

Nice answer. Perhaps "Thus, one is a duplicate value." +/- zero is always a question if the OP wants to or does not care if they are "different numbers". – Afterimage