Final answer:
The first step when the control unit of a computer's CPU starts processing is to fetch an instruction from memory, which precedes interpreting the instruction, performing operations, and writing back results.
Step-by-step explanation:
When the control unit of a computer's CPU swings into action, the first step in the process is to fetch an instruction from memory. This step is crucial before the computer can execute any operations. Once the instruction is fetched, the CPU can then move on to the subsequent steps, which typically involve interpreting the instruction, fetching any necessary data, performing arithmetic or logical operations in the Arithmetic Logic Unit (ALU), and then writing back the result.