A good answer might be:

Since there are 256 possible bit patterns with 8 bits, there could be 128 positive and 128 negative integers.

You may have thought of the sign-magnitude method, discussed below.

Sign-Magnitude Repn

There are many schemes for representing negative integers with patterns of bits. One scheme is sign-magnitude. It uses one bit (usually leftmost) to indicate the sign. "0" indicates a positive integer, and "1" indicates a negative integer. The rest of the bits are used for the magnitude of the number. So -2410 is represented as: 

      1001 1000

      The sign "1" means negative
      The magnitude is 24 (in 7-bit binary)

QUESTION 12:

With 8-bit sign-magnitude representation, what positive integers can be represented and what negative integers can be represented?