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# Digital sum

The digital sum of a set of numbers is the sum of each set of digits independently. That is it is the same as the normal sum except that no carrying is used.

For example in decimal arithmetic, the digital sum of 123 + 789 is 802.

• 3+9=12, discard the 10 leaving 2.
• 2+8=10, discard the 10 leaving 0.
• 1+7=8, there is no carry to discard.
```123
789
---
802
```
More usually the digital sum is calculated in binary where the result only depends upon whether there are an even or odd number of 1s in each column. This is the same function as parity or multiple exclusive ors.

For example:

```011 (3)
100 (4)
101 (5)
---
010 (2) is the digital sum.```

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