Question

State and proof the formula for speed upon kstage pipelining?

Answer 1

1) Improve the hardware by introducing faster circuits.

2) Arrange the hardware such that more than one operation can be performed at the same time.

Since, there is a limit on the speed of hardware and the cost of faster circuits is quite high, we have to adopt the 2nd option.

Pipelining : Pipelining is a process of arrangement of hardware elements of the CPU such that its overall performance is increased. Simultaneous execution of more than one instruction takes place in a pipelined processor.

Let us see a real life example that works on the concept of pipelined operation. Consider a water bottle packaging plant. Let there be 3 stages that a bottle should pass through, Inserting the bottle(I), Filling water in the bottle(F), and Sealing the bottle(S). Let us consider these stages as stage 1, stage 2 and stage 3 respectively. Let each stage take 1 minute to complete its operation.

Now, in a non pipelined operation, a bottle is first inserted in the plant, after 1 minute it is moved to stage 2 where water is filled. Now, in stage 1 nothing is happening. Similarly, when the bottle moves to stage 3, both stage 1 and stage 2 are idle. But in pipelined operation, when the bottle is in stage 2, another bottle can be loaded at stage 1. Similarly, when the bottle is in stage 3, there can be one bottle each in stage 1 and stage 2. So, after each minute, we get a new bottle at the end of stage 3. Hence, the average time taken to manufacture 1 bottle is :

Without pipelining = 9/3 minutes = 3m

I F S | | | | | | | | | I F S | | | | | | | | | I F S (9 minutes)

With pipelining = 5/3 minutes = 1.67m

I F S | | | I F S | | | I F S (5 minutes)

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