Negative exponents can cause problems, a negative exponent in two's complement looks like a large exponent. Thus we will represent the most negative exponent as 00…00b and the most positive exponent as 11…11b.
This convention is call biased notation with the bias being the number subtracted from the normal, unsigned representation. IEEE 754 uses a bias of 127 for single precision. So an exponent of -1 is represented by -1 + 127, or 126d = 0111 1110b. An exponent of 10 is represented by 10+127=137d=10001001.
Now the value represented by a FP number is really: (-1)sign*(1 + mantissa)*2(exponent-bias)
The bias of a double precision number is 1023.