Self Doubt : Pipe lining closed

Question

Given 100 instructions executed on a 5 stage pipeline . probability (p) that an instruction is branch is p. Branch penalty 4.Assuming that each stage of pipeline takes 1 cycle.Calculate total execution time. My query is since first instruction will  take 5 clk so how  to calculate ?  is 5+ 99[(1-p)*1 + p*4] the correct approach ?

Comments

So incorrect .

A couple faults...

(1) why assuming first instruction is not a branch instruction?

(2) even though you are assuming first as branch or non branch, for further instructions, you are only calculating the branch penalty... What about the other stages.

 

A/c to me, one of the correct equation can be 104+400p.

 

 

Please check for any incorrectness if any.

---

If no branch instructions were there then no. of cycles taken would be 5+99*1=104.

Now out of 100, 100p instructions are branch and they take extra 4 cycles. So 4*100p=400p cycles.

So total no. of cycles = 104+400p.

---

cycle per instruction={ p*4+(1-p)*1}

total time = { p*4+(1-p)*1}*100