[OCLUG-devel] calculations one digit at a time

[Michael Elkins]

On Sun, 11 Jul 2004 09:27:44 -0700, James Colannino <james at colannino.org> wrote:
> Hey everyone.  I'm trying to figure out how I'm going to do calculations
> working with one digit at a time (this is so that I can work with fixed
> digit numbers.)  For example:

Are you doing this as a programming exercise?  I'm trying to figure
out why you would want to do integer arithmetic this way?

> 
> 110 + 100
> 
> First, the two 0's in the one's place would be added, then the 0 and the
> 1 in the tens place, and finally the two 1's in the hundreds place.  At
> first glance, it doesn't seem like it would be too difficult.  I would
> assign each individual digit to its own variable and go from there.  The
> problem is, if I add two numbers and I get a number that's equal to 10
> or greater, I'll have to figure out how to borrow, and I'm not quite
> sure how to do that in C.

I believe you mean carry.

> For example:
> 
> 732 + 298
> 
> 8 + 2 is 10, so I would have to move the 1 digit in the tens place over
> one.  Would I maybe convert 10 into a string, split it into the 1 and 0,
> and then convert both back into integers and add them to their
> appropriate places?
> 
> I hope I'm not too out there with my solution :-P  I'm just not quite
> sure what I should do.

Off the top of my head, I'd say to represent each digit as an element
in an array, in reverse order such that index 0 is the ones place, 1
is the tens place, etc.  Then doing carries is pretty easy:

    char a[10]; //operand
    char b[10]; //operand
    char c[11] = {0}; //result

    for (i=0; i<10; i++) {
        c[i] = a[i] + b[i];
        if (c[i] >= 10) {
            c[i+1]++;
            c[i] -= 10;
        }
    }

-Michael