The "biased" exponent has a constant 127 added to it, so for example if the bits are 00000000 the exponent is actually 0-127=-127, if the bits are 10000111 the exponent is 135-127=8, and so forth.

If you want to describe how to get the bit pattern, that's the calculation based on the known exponent. So because 127 - 127 = 0, the bit pattern is zeros. Not the other way around ;)