float

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The largest float could be represented as a 128-bit integer consisting of
24 ones followed by 104 zeroes.

N = (2^24) - 1 in base two is 24 ones. So the largest float is

N * (2^104), i.e. N with another 104 zeroes on the end.

In base ten that's about 3.402823466e38.

The 'most negative float' is the same number times -1.

Here's the relevant #define from FLOAT.H for Visual C++
#define FLT_MAX         3.402823466e+38F