Digital Root/Examples/10010111101 Base 2

Examples of Digital Roots

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 $1$.