Execution time on a pipelined processor, given execution time on a non-pipelined processor

Question

A program executes on a non-pipelined processor in time t. The same program is executed on a m-stage pipelined processor, with each stage delay d. Then, how it is that the execution time of the program on the pipelined processor is given in terms of t, m and d as follows

Execution Time on pipelined processor = (t / m) + d * m

I understand the term "d * m" but how can we have this term "t / m". I can't understand the logic behind this term. Please explain.

Answer 1

A program executes on a non-pipelined processor in time t. {means all instruction is executed in t time}
single instruction take time in execution is m*d {number of stage m, each stage delay is d}
So number of instruction is t/(m*d)

now execution time on pipeline is (n-1+k)*d
where n=#'s of instruction ,   k=stage  ,  d=stage_delay + buffer_delay {in this case ignore buffer_delay}

So [t/(m*d) -1 + m]*d
open bracket (t/m-d+m*d) {this is execution time on pipeline}

if seems anything wrong correct me!!

Comments

Thanks for the explanation. I guess, we can consider that in general case, n>>k and so we can have the execution time on pipeline as n*d  and after putting the values, we can have the execution time, without including the delay, as t/m . Thanks again for the explanation above.