# Digital sum

There are a number of common mathematical meanings of the term **digital sum**:

## Values

- The
**digit sum**- add the digits of the representation of a number in a given base. For example, considering 84001 in base 10 the digit sum would be 8 + 4 + 0 + 0 + 1 = 13. - The
**digital root**- repeatedly apply the digit sum operation to the representation of a number in a given base until the outcome is a single digit. For example, considering 84001 in base 10 the digital root would be 4 (8 + 4 + 0 + 0 + 1 = 13, 1 + 3 = 4).

## Operations

The mathematical operation digital sum in base b can also be called the digital sum. This is where each place is summed independently, ignoring digit carry. For example, 84001 + 56734 = (8 + 5 = 1**3**)(4 + 6 = 1**0**)(0 + 7 = **7**)(0 + 3 = **3**)(1 + 4 = **5**) = 30735.

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