SOLUTION:
We want to multiply the following binary numbers;
[tex]110011_2\times101_2[/tex]It would be really convenient to convert this to base ten, multiplying and then reconverting to base 2;
[tex]\begin{gathered} 110011_2=51_{10} \\ 101_2=5_{10} \end{gathered}[/tex]Thus, the multiplication gives;
[tex]51\times5=255_{10}[/tex]Converting this back to binary we have the result;
[tex]110011_2\times101_2=11111111_2[/tex]