How do you find the sum of binary numbers if you are adding them by hand and there is overflow?

I'm trying to figure out the thought proccess behind something like this:

Consider three 8-bit bytes 01010011, 01100110 and 01110100. The sum of three 8-bit bytes 01010011, 01100110 and 01110100 is as shown below. First, find the sum of first two 8-bit bytes 01010011 and 01100110- 0 1 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 The sum of first two 8-bit bytes 01010011 and 01100110 is 10111001. Now, to the sum obtained, add the third 8-bit byte 01110100. 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 0 Wrap around 1 0 0 1 0 1 1 0 1 Sum 0 0 1 0 1 1 1 0