The information of the first bit is implied via the exponent. Twenty four implied 1's would give you a precision of 76 bits, but you would restrict yourself to

The information of the first bit is implied via the exponent. Twenty four implied 1's would give you a precision of 76 bits, but you would restrict yourself to a very small subset of all possible numbers with that precision. EDIT: Let's put it another way. Assume you have 3 decimal digits of precision for a float. The first digit cannot be zero. Would you then claim that you don't have 3 digits of precision, but rather log(10x10x9,10) = 2.95.., because the first digit only carries 0.95.. digits of information?