Does different Base Year in Price Index affected conversion of nominal value to the real value? I do not have any economics background, but currently I have some data sets regarding price index. I have some doubts regarding if my way of conversion is correct?

I have 4 data set. So let it be DS1, DS1 PI, DS2 and DS2 PI.

Note that DS1 PI and DS2 PI are both different variables price index.

DS1 is price index in Base Year 2012, while DS2 is in Base Year 2014. 

I am using DS1 to convert the nominal value of attribute 1 to a real value. This adjustment is done to convert all DS1 variables to the current real value at May 2015. The formula is shown below.

$$Adjusted Price 1 =\frac{DS1 Variables}{DS 1 PI} \times DS1 PI_{May 2015}$$

Similarly, I am doing the same thing for DS2.

$$Adjusted Price 2 =\frac{DS2 Variables}{DS 2 PI} \times DS2 PI_{May 2015}$$

Then, I would make a comparison between these 2 adjusted price variables. So my question is since the base year are different, would the adjustment to May 2015 be correct? 

Both of the adjusted/real price are now in the same current value and would be comparable. It does not matter if the base year are different in this case?

Sorry if the question is confusing. I would appreciate your help in this matter.

Thanks.
This question might be better suited for a statistics group, but if I understand you correctly you're going to compare two prices from different price indeces and see if there's a difference in the growth? There's really nothing wrong with the reasoning, but you should take the results you get with a grain of salt as you'll be comparing two indeces with different samples.

The different base year is not a problem as long as the variables you're dividing are from the same dataset. When price indices are renewed, the sample is often changed, so this is why you should be aware what you're doing when comparing between different base years.