Chapter 5, Problem 29E

Explanation of Solution

Explanation:

• A non-pipelined Central Processing Unit (CPU) includes four cycles to execute the instructions.
  • Fetch the instruction
  • Decode the instruction
  • Execute the instruction or Perform the operation
  • Store Result
• The pipelined instructions run parallel which requires less time.
• Execution of each instruction requires some amount time whereas the aggregated instructions requires less time.

Assume a k-stage pipeline which includes clock cycle time of ${\text{t}}_{\text{p}}$ with n number of tasks to process.

The time required by the task 1 to complete the process is $\text{k}\text{×}{\text{t}}_{\text{p}}$.

The time required to process the remaining tasks is $\text{(n}-{\text{1)t}}_{\text{p}}$.

The time required to complete n tasks using a k-stage pipeline can be calculated as follows,

$\begin{array}{c}\text{=}\text{k}\text{×}{\text{t}}_{\text{p}}\text{+}\text{(n}-\text{1)}\text{×}{\text{t}}_{\text{p}}\\ \text{=}\text{(k}\text{+}\text{n}-\text{1)}\text{×}{\text{t}}_{\text{p}}\end{array}$

Thus, the time taken to complete n tasks using k-stage pipeline is $\text{=}\text{(k}\text{+}\text{n}-\text{1)}\text{×}{\text{t}}_{\text{p}}$.

The time required by the task 1 to complete the process without using pipeline is ${\text{t}}_{\text{n}}\text{=}\text{k}\text{×}{\text{t}}_{\text{p}}$