The board shall have the following powers:
A. To hear and decide appeals where it is alleged there is an error in any order, requirement, decision or determination made by an administrative official in the enforcement of this title.
B. Where, by reason of exceptional narrowness, shallowness or shape of a specific piece of property at the time of the original adoption of the regulations, or by reason of exceptional topographical conditions or other extraordinary or exceptional situation or condition of a specific piece of property, which condition is not generally prevalent in the neighborhood, the strict application of this title would result in peculiar and exceptional practical difficulties to or exceptional and undue hardship upon the owner of such property, the board is empowered to authorize upon an appeal relating to such property, a variation from such strict application so as to relieve such difficulties or hardship.
C. Upon appeal, the board is empowered to permit the following exceptions:
1. To permit the extension of a district where the boundary line of a district divides a lot in single ownership as shown on record;
2. To permit the reconstruction of a nonconforming building which has been destroyed, or partially destroyed, by fire, or act of God where the board shall find some compelling public necessity requiring a continuance of the nonconforming use, but in no case shall such a permit be issued if its primary function is to continue a monopoly;
3. To permit the erection and use of a building or the use of premises in any location for a public service corporation for public utility purposes which the board deems reasonably necessary for the public convenience or welfare;
4. To interpret the provisions of the title where the street layout actually on the ground varies from the street layout as shown on the map fixing the several districts, which map is attached to and made a part of this title. (Prior code § 11-3-8 (d))