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Sci help me, trying to understand efficient float to string reprsentation.

Pic-related is from talk https://www.youtube.com/watch?v=kw-U6smcLzk

So I'm working with 32bit floats, my raw mantissa is 1677722, appended is 10066330 , raw exponent is 125 and bias subtracted is -2.
I'm getting 0.3f back
https://www.wolframalpha.com/input/?i=10066330+*+2^(-23)+*+2^(-2)

But the formula he proposes to get easy to work integers makes little to no sense to me. He takes mantissa's modulus (abs) value, inverts it to negative and then adds small remainder of what's left after you substract bias (127) from exponent. The 2nd part always will be smaller than mantissa, how he expect to get a positive? Also 2^(16677095) kinda BIG power to begin with:
https://www.wolframalpha.com/input/?i=10066330+*+2^(-10066332)

????