Answer
\[{{222}_{four}}\]
Work Step by Step
To multiply two numbers which are not of base 10, follow the below steps,
To multiply such numbers, multiply it just as it is in base ten. That is first multiply the right most column numbers and continue same as it is done for base ten but in base four there are only 0,1,2 and 3 if multiplication exceed 3 then change it in base four.
\[\begin{align}
{{32}_{four}} & \\
\times {{3}_{four}} & \\
\end{align}\]
To solve this, follow these steps,
\[\begin{align}
& {{3}_{four}}\times {{2}_{four}}={{6}_{ten}} \\
& {{3}_{four}}\times {{3}_{four}}={{9}_{ten}} \\
\end{align}\]
And here 4 is not in base 4, so convert it.
\[{{6}_{ten}}=\left( 4\times 1 \right)+\left( 2\times 1 \right)={{12}_{four}}\]
As, 1 is carry so add 1 in 9, that is \[9+1=10\]
\[{{10}_{ten}}=\left( 4\times 2 \right)+\left( 2\times 1 \right)={{22}_{four}}\]
\[\begin{align}
& \underline{\begin{align}
{{32}_{four}} & \\
\times {{3}_{four}} & \\
\end{align}} \\
& \underline{{{222}_{four}}} \\
\end{align}\]
So, here is the solution of the multiplication.
