Digital sum

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

[edit] Values

• The digit sum - add the digits of the representaion 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).
• The digit part of the digit sum of a number in a given base.^{[citation needed]} For example, considering 84001 in base 10, this would give 3 (8+4+0+0+1 = 13, discard the tens unit leaving 3).

[edit] 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=13)(4+6=10)(0+7=7)(0+3=3)(1+4=5) = 30735.