Since the process is inverted to most cases of scientific notation, as it involves making a faction into an integer rather than turning a large integer into a fraction, exponents are generally negative to move the decimal place to the left; in decimal this would be turning your integer 145 back into the fractional number 1.45 by multiplying it by formula_5. Instead of using an signed leftmost bit the exponent is instead biased, giving 32-bit float exponents a range of formula_6 to formula_7. The output value of the biased exponent can be found by adding 127 to it: