Digital Root/Examples

Examples of Digital Roots

$34716$ Base $10$

In conventional base $10$ notation, we have:

$\map {s_{10} } {34716} = 3 + 4 + 7 + 1 + 6 = 21$

and then:

$\map {s_{10} } {21} = 2 + 1 = 3$.

So the digital root of $34716$ (base $10$) is $3$.

$10010111101$ Base $2$

In binary notation, we have:

\(\ds \map {s_2} {10010111101_2}\)

\(=\)

\(\ds 1 + 0 + 0 + 1 + 0 + 1 + 1 + 1 + 1 + 0 + 1\)

\(\ds = 7 = 111_2\)

\(\ds \map {s_2} {111_2}\)

\(=\)

\(\ds 1 + 1 + 1\)

\(\ds = 3 = 11_2\)

\(\ds \map {s_2} {11_2}\)

\(=\)

\(\ds 1 + 1\)

\(\ds = 2 = 10_2\)

\(\ds \map {s_2} {10_2}\)

\(=\)

\(\ds 1 + 0\)

\(\ds = 1 = 1_2\)

It is pretty obvious that the digital root of any non-zero number in base $2$ is always $1$.