Suppose an instruction requires four cycles to execute in an unpipelined CPU: one cycle for instruction fetch, one for decode and operand fetch, one for the ALU operation, and one for result storage. In a CPU with a four-stage pipeline, the instruction also requires four cycles to complete. How, then, can we say that pipelining accelerates program execution?

Pipelining accelerates program execution by allowing multiple instructions to be processed simultaneously at different stages of completion, rather than processing each instruction one at a time from start to finish.

Think of pipelining like an assembly line in a factory. In an unpipelined CPU (like a traditional factory where one product is made from start to finish before the next one is started), an instruction goes through all four stages (fetch, decode, execute, and store) one after the other. This means that for each instruction, the CPU completes one full cycle for each stage, taking a total of four cycles to complete an instruction.

However, in a pipelined CPU (similar to an assembly line where different parts of a product are assembled simultaneously), once the first instruction has been fetched and moves onto the decode stage, the second instruction can be fetched in the next cycle without waiting for the first instruction to complete all of its stages. As a result, after the initial filling of the pipeline (four cycles in this case), a new instruction can complete every cycle.

For example, let's look at the timeline for a four-instruction sequence in both CPUs:

Unpipelined CPU (one instruction at a time): Instruction 1: Fetch - Decode - Execute - Store (4 cycles) Instruction 2: Fetch - Decode - Execute - Store (4 cycles) Instruction 3: Fetch - Decode - Execute - Store (4 cycles) Instruction 4: Fetch - Decode - Execute - Store (4 cycles) Total: 16 cycles

Pipelined CPU (a new instruction enters the pipeline every cycle): Cycle 1: Instruction 1: Fetch Cycle 2: Instruction 1: Decode | Instruction 2: Fetch Cycle 3: Instruction 1: Execute | Instruction 2: Decode | Instruction 3: Fetch Cycle 4: Instruction 1: Store | Instruction 2: Execute | Instruction 3: Decode | Instruction 4: Fetch After the pipeline is filled (Cycle 5 onward): New instruction can complete every cycle Total for 4 instructions: 7 cycles (4 to fill the pipeline + 3 for the remaining instructions to complete)

So, while it takes the same amount of time for each instruction to pass through all the stages in both types of CPU, the key advantage of pipelining is that the CPU throughput is increased, meaning more instructions are completed in the same amount of time, because they are overlapped in execution.

Extra: Pipelining is an important concept in computer architecture that exploits parallelism in the instruction processing workflow. While pipelining improves the throughput (the number of instructions processed per unit of time), it's essential to understand that it does not reduce the individual instruction latency (the time to complete a single instruction from start to finish).

Key concepts related to pipelining in CPUs include:

1. Throughput: The rate at which the processor can complete instructions.

2. Latency: The time it takes for a single instruction to pass through the entire pipeline from start to finish.

3. Hazard: A condition that causes a stall or delay in the pipeline, often due to dependencies between instructions. Hazards can be data hazards, structural hazards, or control hazards.

4. Stall: A cycle where the pipeline does not progress due to a hazard.

Effective pipelining aims to minimize stalls and hazards, allowing instructions to flow through the pipeline as smoothly and continuously as possible. Techniques like instruction reordering, forwarding, and branch prediction are used to optimize pipeline performance. Understanding these concepts can help students grasp how modern CPUs efficiently process a high volume of instructions.