ALU

Arithmetic-Logic Unit: the portion of a computer's central processing unit that performs integer arithmetic and logical operations, such as bitwise AND, OR, NOT, and XOR. The instruction decode logic of the CPU determines which particular operation the ALU should perform, the source of the operands, and the destination of the result.

The width in bits of the words which the ALU handles is usually the same as that quoted for the processor as a whole whereas its external busses may be narrower. Floating-point operations are usually done by a separate floating-point unit. Some processors use the ALU for address calculations, such as incrementing the program counter, others have separate logic for this.

ALU is short for Arithmetic Logic Unit.
This is the place where the heavy duty power of the computer chip hums. In it are comparators, adders, barrel shifters, complimenters, transfer gates, registers and lots of control logic.
Some of the registers are pretty standard: (the following list is based on a CISC ALU)

• One or more accumulators (such as EAX,ECX,EDX)
• One or more index registers (such as ESI, and EDI)
• One or more address or base registers (EBX, EBP)
• A program status register (such as FLAGS)
• A program counter (such as EIP)
• Sometimes control registers (like CR0 and CR1)

In a RISC ALU all the registers may have the same, though expanded, collection of functions. Normal operations of an ALU are add, move, compare, branch, and, depending on the type, write and read.
Input and output are sometimes mapped to memory locations.
The control unit usually handles all the flow and decoding of tasks to do. Giving the ALU specific details on what to do.