Next, we will consider how to make a program that adds two numbers, from 0 to 9 together.

Again, we will represent the numbers 0 through 9 with only 1's and 0's as indicated in the following table.

Table 6

                         Number  Representation
                              0  0000
                              1  0001
                              2  0010
                              3  0011
                              4  0100
                              5  0101
                              6  0110
                              7  0111
                              8  1000
                              9  1001

Next, we need a table that shows the answer for each possible pair of numbers from 0 to 9. This is the addition table we studied so hard to learn in grade school and is reproduced below.

Addition Table

           +   0  1  2  3  4  5  6  7  8  9

           0   0  1  2  3  4  5  6  7  8  9
           1   1  2  3  4  5  6  7  8  9 10
           2   2  3  4  5  6  7  8  9 10 11
           3   3  4  5  6  7  8  9 10 11 12
           4   4  5  6  7  8  9 10 11 12 13
           5   5  6  7  8  9 10 11 12 13 14
           6   6  7  8  9 10 11 12 13 14 15
           7   7  8  9 10 11 12 13 14 15 16
           8   8  9 10 11 12 13 14 15 16 17
           9   9 10 11 12 13 14 15 16 17 18

Next, we rewrite the addition table above as below.

Addition Table Listing

                             0 + 0 = 00
                             0 + 1 = 01
                             0 + 2 = 02
                             0 + 3 = 03
                             0 + 4 = 04
                             0 + 5 = 05
                             0 + 6 = 06
                             0 + 7 = 07
                             0 + 8 = 08
                             0 + 9 = 09
                             1 + 0 = 01
                             1 + 1 = 02
 
                                 .
                                 .
                                 .
 
                             8 + 9 = 17
                             9 + 0 = 09
                             9 + 1 = 10
                             9 + 2 = 11
                             9 + 3 = 12
                             9 + 4 = 13
                             9 + 5 = 14
                             9 + 6 = 15
                             9 + 7 = 16
                             9 + 8 = 17
                             9 + 9 = 18

Only some of the table elements are listed above to save space.

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