Your (informal, ungraded, but important to do) homework is:

  Assume you are adding two binary numerals; you are somewhere in the middle
  of the process and therefore have to add the current two digits in the column
  (call them P and Q) and also add in the carry from the previous column (call
  it C). You need to produce TWO answers: the result in the current column (call 
  it R) and the new carry for the next column (call it C' "C-prime").
  
  You should write out formulas for R and C' in terms of P, Q and C, using 
  logical/Boolean operators (and, or, not, xor, etc.). By way of a hint, when we
  did this for the case of two columns and NO carry (on input), we found that 
  the result value was the XOR of the two inputs and the carry (ofr the next column)
  was the AND of the two inputs. Thus we might write:
  
    R  = P XOR Q
    C' = P AND Q
    
  Your answer(s) will thus look something like this:
  
    R  = ... P ... XOR ... Q ... C ... NOT ... (or whatever)
    C' = ... P ... AND ... Q ... XOR ... C ... (or whatever)
    
  You can use any symbols you want for the operators (&&, ||, ^, plus-with-a-circle,
  etc.) as long as you can promounce them or explain them on Tuesday.
  
  You can even draw them as circuits, if you like, on the simulator at this address:
  
    <http://www.course.com/downloads/computerscience/aeonline/7/1/>