Formula of MIPS (million instructions per second)

Question

Could you please help me to understand the mathematics behind MIPS rating formula?

The performance of a CPU (processor) can be measured in MIPS. The formula for MIPS is: $$\text{MIPS} = \frac{\text{Instruction count}}{\text{Execution time} \times \ 10^6}$$

Example: say, there are 12 instructions and they are executed in 4 seconds. So the CPU's performance is $\frac{12 \text{ instructions}}{4 \text{ sec}} = 3 \text{ instr/sec}$. MIPS would be $3\times10^{-6}$.

Question: How do we go from 3 instructions per second to millions instructions per second? What is the logic behind dividing by $10^6$ = 1 million?

PS: Sorry for asking this kind of questions here. I asked some computer scientists and I am still looking for an explanation.

Answer 1

Typically you would be able to execute a lot more than 12 instructions in 4 seconds. For example, suppose you execute 8,000,000 instructions in 4 seconds. Dividing those number gives 2,000,000 instructions per second.

Now 2,000,000 instructions per second is the same thing as 2 million instructions per seconds -- just try to pronounce it! In order to find out how many millions you have, divide the raw number by one million.

That's not very different from finding out how many dozen eggs you have if you have 72 eggs. A dozen is 12, so 72 eggs is $\frac{72}{12}=6$ dozen eggs. For your MIPS example the large unit you choose just happens to equal $10^6$ of the smaller unit rather than 12, but the principle is the same.