The first thing to notice is that a (not subnormal) floating point number can be compared as such: you look at the exponent bits, and pick the one that has the greater exponent. If they are equal, then look at the mantissa, which is always between 1 and 2, and pick whichever one is larger. Since the exponent comes before the mantissa bits in the bit representation of a floating point number, it has "higher significance" when interpreted in fixed point. If we used two's complement to represent the exponent negative exponents would "look larger" than positive ones, despite them being smaller. But if we used a biased representation, where we shift the range so that there can only be a positive number in that field, and the smaller negative exponents can actually be small and the positive exponents are be larger than those so we can compare them directly.