Find average CPI of non-pipeline CPU(assume ideal case for pipelining)?

Question

Consider a 5 stage instruction pipeline having latencies (in ns) 1, 2, 3, 4 and 5 respectively.
Find average CPI of non-pipeline CPU when speed up achieved with respect to pipeline is 4
(assume ideal case for pipelining)?
(a) 1.23
(c) 1.66
(b) 1.33
(d) 1.73

Comments

b) 1.33???

---

yes,can you just help to get it with proper formula and its explanation,Thanks :)

---

speedup=tn/tp=CPI*INSTRUCTION*CYCLETIME/INSTRUCTION*CYCLETIME

4              =CPI(1+2+3+4+5)/1*5

20/15=4/3=1.33

Answer 1

T_non-pipeline = sum of all stages delay = 15ns

T_pipeline  = max delay among all stages delay = 5ns

Given speedup = 4

Speedup = $\frac{\text{Execution of non pipeline}}{\text{Execution of pipeline}}$

Execution of non pipelined = CPI_{non-pipelined} * Cycle time

Execution of non pipelined = CPI_{non-pipelined} * 15ns

Now,

Execution of pipelined = CPI_pipelined * cycle time 

In pipelined ideally CPI_pipelined = 1

Execution of pipelined = 1 * 5ns

4 = (CPI_{non-pipelined} *15)/(1*5)

CPI_{non-pipelined} = 4/3

CPI_{non-pipelined} = 1.33

Ans = 1.33

Comments

Thanks, Can you please answer this https://gateoverflow.in/156074/what-is-the-maximum-speedup-achieved-in-new-pipeline-system

---

How can we take sum of all stage delays (i.e., Execution time of one instruction in non-pipelined architecture) as Cycle Time?