How do cpu calculator and controllers collaborate?

The cpu calculator and controller work closely together through a closed-loop process of fetch decode execute write back, as follows:
Instruction fetch phase: The controller retrieves the instruction to be executed from memory, stores it in the instruction register, and updates the program counter to point to the next instruction address.
Decoding stage: The controller parses instructions through an instruction decoder, identifies operation types and operands, and generates corresponding control signals.
Execution phase: The controller sends control signals to the arithmetic unit, and the ALU of the arithmetic unit completes the specified arithmetic/logical operations. During the operation, data can be temporarily accessed through registers.
Write back stage: The arithmetic unit feeds back the calculation result to the controller, which completes the storage of the result and updates the status flag. Then, it automatically enters the instruction retrieval process of the next instruction, and completes all tasks in a loop.
The division of labor between the two is clear: the controller serves as the command center responsible for scheduling, the arithmetic unit serves as the execution unit responsible for data processing, and cooperates with the register group to jointly implement the complete instruction execution process of the CPU.