Arithmetic Logic Unit (ALU) and Control Unit (CU)
The Arithmetic Logic Unit (ALU) is one of the most important parts of the CPU.
In its most basic form an ALU can simply add or subtract two numbers (in binary) and output the result. A slightly more advanced ALU can also output a set of flags (as a 1 or 0) that show if an overflow has happened (binary addition and overflow is explained here)
Modern ALUs can do quite a bit more than these basic operations. They can multiply and divide numbers and they can do Logic Operations such as AND, OR, NOT, and more complex combined ones too.
Most modern ALUs are able to work with 32bit or 64bit binary numbers.
The Control Unit (CU)
The control unit obtains data and instructions from memory, decodes the instructions into commands / signals and Controls the transfer of instructions and data in the CPU (between the different registers and the caches and RAM)
