Pipelining

Let's do some math now to find how fast pipelining works compared to sequential exeuction.

Suppose that some code has $n$ instructions, and that the CPU can break the fetch-decode-execute cycle into $k$ small steps (the previous slide introduced 6 steps, for example.) Also, suppose that each small step needs only one clock cycle to complete.

• If we run our instructions one-by-one, without pipelining, we will need a total of $n\cdot k$ clock cycles to run these $n$ instructions.
• However, with pipelining, we notice from the previous image that the number of clock cycles we used was $6 + 4 - 1 = 9$ clock cycles ($6$ was the number of small steps, and $4$ was the number of instructions.
  In general, if the CPU uses pipelining, the number of clock cycles will be equal to $k + n - 1$.

Note that, if $k \ge 3$ and $n \ge 3$, the quantity $k + n - 1$ is much smaller than $n\cdot k$, which means that pipelining is indeed faster comparing to sequential exeuction! (Remember: fewer clock cycles needed = faster execution.)