Definition:Digit Sum

Definition
Let $n \in \Z: n \ge 0$.

The digit sum of $n$ to base $b$ is the sum of all the digits of $n$ when expressed in base $b$.

That is, if:
 * $\displaystyle n = \sum_{k \mathop \ge 0} r_k b^k$

where $0 \le r_k < b$, then:
 * $\displaystyle s_b \left({n}\right) = \sum_{k \mathop \ge 0} r_k$

Examples
In conventional base $10$ notation, we have:


 * $s_{10} \left({34716}\right) = 3 + 4 + 7 + 1 + 6 = 21$

In binary notation, we have:
 * $s_{2} \left({10010111101_2}\right) = 1 + 0 + 0 + 1 + 0 + 1 + 1 + 1 + 1 + 0 + 1 = 7$

Also see

 * Definition:Digital Root