I was reading my notes and came across the following
The sign of the exponent e usually is not encoded by a complement, but the so-called bias N (also referred to as excess-N). This means that e = N stands for 0, all values e > N for positive exponents and all values e < N for negative exponents.
It was followed by this example:
Example: An exponent e of 5 bits, bias 16.
value of e = meaning
$00000_{2}$ = $-16_{10}$
....
$01111_{2}$ = $-1_{10}$
$10000_{2}$ = $0_{10}$
....
$11111_{2}$ = $15_{10}$
I understand that the above table is represented in 2's complement using 5 bits but how is it that $11111_{2}$ is now equivalent to $15_{10}$? When I convert $11111_{2}$ to decimal I get 31 at http://www.mathsisfun.com/binary-decimal-hexadecimal-converter.html.