Let's answer our second question first. All computers have a Unit which performs arithmetic and logical functions. This Unit is called as Arithmetic and Logic Unit (ALU). However how will computer decide what operation is to be carried out by ALU or we can say who will interpret the operation that is to be performed by ALU?
This interpretation is carried out by Control Unit of computer. The control unit recognizes the binary form of instruction as well as interprets instruction to generate control signals. These control signals then direct ALU to carry out a particular arithmetic or logic function on data. Thus by changing control signal desired function can be performed on data. Or on the other hand the operations that require to be performed on the data can be achieved by providing a set of control signals. So for a new operation one just needs to change set of control signals.