Total numbers represented in IEEE single precision and double precision

Question

How many total numbers can be represented in IEEE single precision format and double precision format?

single precision - 1 sign bit, 8 exponent , 23 bit mantissa double precision - 1 sign bit, 11 exponent bit, 52 mantissa

Answer 1

Single precision:

23 bit mantissa: 2^23 possibilities 1 bit sign: 2 possibilities 8 bit exponent: 2^8 - 1 possible exponents (1 exponent used for special cases such as NaN)

So, total numbers that can be represented = 2^23 * 2 * (2^8 - 1)

I hope I'm not missing anything.