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.

```           +   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.

```                             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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