The assessors, under the direction of the commissioner, shall assess all the real property in the several districts that may be assigned to them by the commissioner and shall prepare the assessment rolls. The term "assessment" shall mean a determination by the assessors of (a) the taxable status of real property as of the taxable status date; and (b) the valuation of real property, including the valuation of exempt real property, and where such property is partially exempt, the valuation of both the taxable and exempt portions.