title: Running time analysis for addition of two n digit numbers
body: <p>I'm trying to see what is the time complexity of addition of two numbers. It is written here as addition being n square. <a href="http://compgeom.cs.uiuc.edu/~jeffe/teaching/algorithms/notes/05-dynprog.pdf" rel="nofollow">Algo Notes</a></p>
  
  <p>Page number 4 second paragraph.</p>
  
  <p>Now if I take 99 + 99 as  I 'll be doing two addition operations and two carry operations + adding carry from prev to new result and combining everything.</p>
  
  <p>I'm not sure how can I say this is n square.</p>
  
  <p>That makes me think that I should possibly represent the numbers in binary which would make 01100011 in 8 bits which would lead to 8 additions plus 4 carry additions. This seems like n square but I'm not sure about it.</p>
  
  <p>Is there a different way to look at this? How is it n square? You can run a loop over each digit and add the positional place i.e 10*sum+100*sum etc, but I can very well do this in one single for loop.</p>