Let us consider first the problem of doing addition in decimal. Firstly we need to develop the decimal addition table:
0  1  2  3  4  5  6  7  8  9  

0  00  01  02  03  04  05  06  07  08  9 
1  01  02  03  04  05  06  07  08  09  10 
2  02  03  04  05  06  07  08  09  10  11 
3  03  04  05  06  07  08  09  10  11  12 
4  04  05  06  07  08  09  10  11  12  13 
5  05  06  07  08  09  10  11  12  13  14 
6  06  07  08  09  10  11  12  13  14  15 
7  07  08  09  10  11  12  13  14  15  16 
8  08  09  10  11  12  13  14  15  16  17 
9  09  10  11  12  13  14  15  16  17  18 
Where in each square we have two parts:
Carry Digit  Units Digit 

The algorithm for integer (whole number) addition is then:

For more help on arithmetic number tables and arithmetic in various bases click here.
** What is the complexity of this algorithm?
Last updated 2002/02/05
© J.A.N. Lee, 20002002.