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According to this wikipedia article the maximum single precision is 7f7fffff. Can some explain me why it is (7f7fffff)16 and not (7fffffff)16?

(7f7fffff)16 = (0111 1111 0111 1111 1111 1111 1111 1111)2
(7fffffff)16 = (0111 1111 1111 1111 1111 1111 1111 1111)2

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The second exponent is FF, which signals NaN according to Wikipedia, and so the highest exponent is only FE. This is verified by the following C code snippet:

unsigned int i = 0x7FFFFFFF;
float f = *(float*)&i;

If you print f you get nan.

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