Answer
The base two-numeral is\[{{111000}_{two}}\].
Work Step by Step
To convert base ten numeral to any other base,divide given numeral with the greatest number in the power of base value as shown below:
\[32\overset{1}{\overline{\left){\begin{align}
& 56 \\
& \underline{32} \\
& 24 \\
\end{align}}\right.}}\]
Now, divide 24 by 16:
\[16\overset{1}{\overline{\left){\begin{align}
& 24 \\
& \underline{16} \\
& 8 \\
\end{align}}\right.}}\]
Divide 8 by 8:
\[8\overset{1}{\overline{\left){\begin{align}
& 8 \\
& {\underset{\scriptscriptstyle-}{8}} \\
& 0 \\
\end{align}}\right.}}\]
Here, the base value of resultant numeral is \[2\].So, powers of base numerals are \[{{2}^{0}},\,{{2}^{1}},\,{{2}^{2}},\,{{2}^{3}},....\]which can be written as\[1,\,2,4,8,16,32,....\]when solved.
Now, use the quotients of each division base ten numeral can be found as follows:\[\begin{align}
& 1\times 32\,+1\times 16\,+1\times 8\,+0\times 4+\,0\times 2+0\times \,1\,=1\times {{2}^{5\,}}+\,1\times {{2}^{4}}\,+1\times {{2}^{3}}\,+0\times {{2}^{2}}+0\times {{2}^{1}}+0\times {{2}^{0}} \\
& ={{111000}_{\text{two}}}
\end{align}\]
The base two-numeral is\[{{111000}_{two}}\].
