In a 32-bit floating point, it was said that the highest possible value is 3.4028235 x 10^38. However, when we evaluate this, it will be equal to 340282346638528860000000000000000000000. This whole number would require more than 100 integer bits right? My question is: If that is the case, how come this number requiring more than 100 bits fitted in a 32-bit floating point?
In: 3
In floating point the number is stored in a similar fashion to the scientific notation example you gave, only that the powers are in binary not decimal. There are certain number of bits for the mantissa (23 in single precision), the remaining bits for the exponent (8) and one for the sign. This allows a wide range of orders of magnitude to be encoded in the same list of numbers. This advantage is lost when converted to an integer.
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