| The complement of a number (on this
machine) is the difference between that
number and 9. Using this system, the
complement is added to the value in
each column, including any column with
a zero. However, to finish the calculation,
a 1 has to be added to the result. |
| |
| This could have been avoided if the
right-hand column had been marked with
complements of 10 instead of 9, with
zero treated as 10. |
| |
| The complements would have looked
like this: |
| |
| 0 9 |
|
0 9 |
|
0 9 |
|
0 9 |
|
0 9 |
|
0 9 |
|
1 9 |
| 1 8 |
|
1 8 |
|
1 8 |
|
1 8 |
|
1 8 |
|
1 8 |
|
2 8 |
| 2 7 |
|
2 7 |
|
2 7 |
|
2 7 |
|
2 7 |
|
2 7 |
|
3 7 |
| 3 6 |
|
3 6 |
|
3 6 |
|
3 6 |
|
3 6 |
|
3 6 |
|
4 6 |
| 4 5 |
|
4 5 |
|
4 5 |
|
4 5 |
|
4 5 |
|
4 5 |
|
5 5 |
| 5 4 |
|
5 4 |
|
5 4 |
|
5 4 |
|
5 4 |
|
5 4 |
|
6 4 |
| 6 3 |
|
6 3 |
|
6 3 |
|
6 3 |
|
6 3 |
|
6 3 |
|
7 3 |
| 7 2 |
|
7 2 |
|
7 2 |
|
7 2 |
|
7 2 |
|
7 2 |
|
8 2 |
| 8 1 |
|
8 1 |
|
8 1 |
|
8 1 |
|
8 1 |
|
8 1 |
|
9 1 |
| 9 |
|
9 |
|
9 |
|
9 |
|
9 |
|
9 |
|
0 |
|
| |
| Using the revised table above, to
deduct 345 from 975 we would add the
red figures 9999345
where the carry will result in the answer
0000630. |
| |
| Another way of looking at complements
is to see the complement of any number,
of any number of digits, as the difference
between the number and 10 to the power
of the number of digits. |
| |
| The complement of 4 is therefore 10
- 4 or 6, the complement of 44 is 100
- 44 or 56, the complement of 1234 is
10000 - 1234 or 8766. You will see that
these match the revised table. |
| |
| The complement of 0000345 (padded
with zeroes because we have a seven
column adding machine) is 1000 - 345
or 0000655, the values in black alongside
the red 9999345
used above. |
