Two's complement maximum and minimum
Look at 3 bits representation:

000 = 0
001 = 1
010 = 2
011 = 3
100 = -4
101 = -3
110 = -2
111 = -1


Half of the numbers are starting with '1', which is the sign bit. So half of the numbers are negative. It means that we have \$(2^x)/2 = 2^{(x-1)}\$ negative numbers. The rest are positive and zero.