Definition:Digit Sum
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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:
- $\ds n = \sum_{k \mathop \ge 0} r_k b^k$
where $0 \le r_k < b$, then:
- $\ds \map {s_b} n = \sum_{k \mathop \ge 0} r_k$
Examples
In conventional base $10$ notation, we have:
- $\map {s_{10} } {34 \, 716} = 3 + 4 + 7 + 1 + 6 = 21$
In binary notation, we have:
- $\map {s_2} {10010111101_2} = 1 + 0 + 0 + 1 + 0 + 1 + 1 + 1 + 1 + 0 + 1 = 7$
Also see
Sources
- Cooper, Topher and Weisstein, Eric W. "Digit Sum." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DigitSum.html