I am trying to understand the limits of the floating point representation.
On a 32-bit computer with 7 bits for the exponent and 24 bits for the mantissa, I want to know the biggest and smallest numbers.
My calculation:
Base 2
Biggest positive number = $ + 1 \times 2^{127} $
Smallest positive number = $ + 2^{-24} \times 2^{-127} $
Biggest negative number = $ - 2^{-24} \times 2^{-127} $
Smallest negative number = $-1 \times 2^{127}$
Decimal
Biggest positive number = $ +1 \times 10^{38} $
Smallest positive number= $ + 10^{-7} \times 10^{-38} $
Biggest negative number= $ - 10^{-7} \times 10^{-38} $
Smallest negative number = $ -1 \times 10^{38} $
Is this a correct calculation?