This is a kind of open ended question when you consider modern CPUs. All CPUs consist of:
1. A Arithmetic-Logic Unit that does in simplest form addition of two values and comparison of two values,
2. Registers that hold instructions to be executed by the CPU and holds data that is acted upon by the CPU and where the results of that action are stored
3. A control unit that determines the next instruction to execute and initiates the action of loading that instruction into one of the registers described in 2 above.
Today's more powerful computers routinely also have:
1. A Floating Point Processor that can do non integer mathematics,
2. The actual circuitry for the operations it is hard wired to be capable of performing
3. Microcode for operations programmed into it such as advanced mathematical functions like square root, exponentials, logarithms, trigonometric functions, ...
4. Bus logic
5. A processor for performing operations on multiple sets of data simultaneously using vectors