Effect of mutation in DNA sequence on transcription factor binding sites How much does a single mutation/alteration of a nucleotide affect the presence of a transcription factor binding site (TFBS)? 
I am from computer science background(Obviously). 
I want to make a general assumption about the number of mutated bases in a TFBS to minimize the binding affinity?
I haven't worked on TFBSs but I really, really doubt you will be able to do this. In mutations, like in real estate, it's location, location, location. It isn't a question of how many mutations but what mutations and where. TFBSs are usually described using position weight matrices, precisely because that's how you can show the importance of different changes in different positions. 

Here are a couple of random Google image search results for "transcription factor binding sites logo":



(This was taken from here and you might want to read through it.)


(source: Front. Genet., 23 February 2016 | https://doi.org/10.3389/fgene.2016.00024)

The main take home messages from these images are:


Different positions have different importance and potential to disrupt binding. In the first image, I would expect that changing the T at position -3 to anything else would be pretty bad. However, changing an A to a T at -8 would likely be neutral. 
Different TFs have very different binding sites and very different binding site lengths.  Look at panel B of the second image. That one appears to be a very conservative site and likely any change would be deleterious. Conversely, changing any of the nucleotides of the 17bp spacer shown in panel A would likely not be important as long as you don't change the length. 


Please note that I have not done more than glance at the sources I took these from, so my inferences may well be wrong, I only use them to illustrate the general point: you cannot really put a number to this. You will always need to look at each specific change and each specific position. In some cases, a single change can disrupt binding while in others multiple changes might have no effect at all. 



You might want to look into TFBS databases like JASPAR or TRANSFAC.