Exponent of what? I assume you mean "find a negative exponent for the base 2 that results in a value between 0 and 1/2."
1
Note that 1/4 lies between 0 and 1/2, and that 1/4 is equal to ------- = 1/4
2
2
Note also that 2^(-2) = 1/4.
Therefore, the negative exponent to the base 2 that produces a fraction between 0 and 1/2 is -2.