\(10101_{2} \rightarrow X_{3}\)
To convert \(10101_{2}\) to a number in base 3 , we first convert to base 10 and from the base 10 number. we get the base 3 number.
\(10 \mathrm{IOl}_{2} \rightarrow \mathrm{Y}_{10}\)
then.
\begin{aligned}
Y_{10} &=1+0^{5} 120^{1} \\
&=1 \times 2^{4}+1 \times 22+1 \times 2^{0} \\
&=16+4+1=21_{10}
\end{aligned}
\(21_{10} \rightarrow X_{3}\)
then.
\begin{array}{l|lll} 3 & 21 & & \\ \hline 3 & 7 & \(r\) & 0 \\ 3 & 2 & \(r\) & 1 \\ 0 & 0 & \(r\) & 2 \end{array}
\(X_{3} \Rightarrow 210_{3}\)