There is a big difference between these components. Both of them are part of central processor unit but control unit is responsible for generating control signals to all parts of cpu, to handle interrupts, to deal with registers etc. Arithmetic logic unit is part which does arithmetic and logic operations (for example, arithmetic operations are add,subtract,add with carry,subtract with carry,divide... and logic operations are AND,OR,XOR,NOT,NAND,NOR...).
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A CPU (Central Processing Unit) is the primary component of a computer that performs most of the processing inside a computer. It consists of the control unit, arithmetic logic unit, and registers. The control unit is a component of the CPU that manages the execution of instructions by decoding and coordinating the operations of the other components. In simpler terms, the CPU is like the brain of the computer, while the control unit is like the manager that directs and controls the flow of data and instructions within the CPU.
The CU decodes instructions, then tells the other Units (including the ALU) what to do.