Let us consider first the problem of doing addition in decimal. Firstly we need to develop the decimal addition table:

Where in each square we have two parts:

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

Treat blanks as 0; Arrange the two numbers to be added so that their lowest order digits are aligned one above the other; Reserve a blank row above the two numbers (the carry row); Reserve a blank row below the two numbers to receive the result: Carry Addend 1 Addend 2 Units Starting from the rightmost column of digits, repeat: Use the addition table to determine the "carry digit" and the "units digit"; Place the units digit in the result row below the two digits being added; Place the carry digit in the carry row in the column to the left of the two digits being added; Until all the columns of digits have been added together; Repeat the same process again using the carry row of digits and the result row until the carry row is empty. [**]

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, 2000-2002.