Anagative exponent that has a value between 0 and 1/2

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.