Answer
The required binary representation is $1001100100$.
Work Step by Step
Convert the decimal number into binary number as,
$\begin{align}
& 2\left| \!{\underline {\,
612 \,}} \right. \text{ remainders} \\
& 2\left| \!{\underline {\,
306 \,}} \right. \text{ }0 \\
& 2\left| \!{\underline {\,
153 \,}} \right. \text{ }0 \\
& 2\left| \!{\underline {\,
76 \,}} \right. \text{ 1} \\
& 2\left| \!{\underline {\,
38 \,}} \right. \text{ }0 \\
& 2\left| \!{\underline {\,
19 \,}} \right. \text{ }0 \\
& 2\left| \!{\underline {\,
9 \,}} \right. \text{ 1} \\
& 2\left| \!{\underline {\,
4 \,}} \right. \text{ 1} \\
& 2\left| \!{\underline {\,
2 \,}} \right. \text{ }0 \\
& 2\left| \!{\underline {\,
1 \,}} \right. \text{ }0 \\
& \text{ 0 1} \\
\end{align}$
Read the remainder from bottom to top as
${{612}_{10}}={{1001100100}_{2}}$
Hence the binary number is $1001100100$.
