Hex addition again
Why is $A + $8 = 2 with a carry out of 1? The carry out has a weight equal to the BASE (in this case 16). The digit that gets left is the excess (BASE - sum). $A + $8 = 10 + 8 = 18.
18 is GREATER than 16 (BASE), so need a carry out!
Excess is 18 - BASE = 18 - 16 = 2, so ‘2’ is digit.
Exactly the same thing happens in Decimal. 5 + 7 = 2, carry of 1. 5 + 7 = 12, this is greater than 10!. So excess is 12 - 10 = 2, carry of 1.