Question

a machine operates several instructions with mips pipeline. there are five pipeline stages in the mips pipeline, including if, id, ex, mem, and wb. we assume one clock cycle for each stage. how many clock cycles will be needed to complete 10 instructions if the machine is non-pipelined? how many clock cycles will be needed to complete 10 instructions if the machine uses 5-stage mips pipeline? please list your assumptions explicitly. if the mips pipeline has k stages instead of 5, how many clock cycles will be needed to complete n instructions? please list your assumptions explicitly.

Answer 1

For a non-pipelined machine, 10 instructions require 50 clock cycles. In a 5-stage MIPS pipeline, it may take around 12-15 clock cycles. The general formula for k-stage pipelines is n + (k - 1) clock cycles.

Non-Pipelined Machine:

- Assumption: In a non-pipelined machine, each instruction goes through all stages sequentially without overlapping.

- Calculation: For 10 instructions, each taking 5 clock cycles (one for each stage), the total clock cycles needed would be 10 × 5 = 50 clock cycles.

5-Stage MIPS Pipelined Machine:

- Assumption: In a 5-stage MIPS pipeline, instructions overlap in different stages, and each stage takes one clock cycle.

- Calculation: Since the pipeline processes instructions concurrently, the total clock cycles needed would be slightly more than the number of instructions. It is generally considered that there's a pipeline startup overhead and that not all stages are fully utilized. For 10 instructions, it might be around 12-15 clock cycles.

General Formula for k-Stage MIPS Pipeline:

- Assumption: Each stage of the pipeline takes one clock cycle, and the pipeline is fully utilized.

- Calculation: The number of clock cycles needed to complete n instructions in a k-stage MIPS pipeline can be estimated as n + (k - 1). This accounts for the pipeline startup overhead and the concurrent processing of instructions in the pipeline stages.

Remember, these are simplified calculations, and actual performance may vary based on specific architecture details, pipeline hazards, and efficiency in instruction execution.