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How many IEEE single precision floating point number are in the range [1,2]?

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As we need numbers in positive range, sign bit will stay  0.

about Exponent, we will have to set  it to 127 (representation of 0 in Excess 127)

about mantissa, as numbers are of the form (-1)sign * (1,M) * 2(exponent-127)   ,1 is implicit.

so we have 2 possibilities now  for filling each digit of mantissa(either 0 or 1), making 223 numbers in which '1' is also counted.

Now, as its closed interval, we need to count '2' as well. so, Total 223 + 1 numbers we can represent in the given range.

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