Binary multiplication

It turns out binary multiplication has easier rules when compared to decimal multiplication. The same general principle applies. For example, $1011_{2}\times110_{2}$ is $1011_{2}\times(100_{2}+10_{2}+0_{2})$, which then becomes $1011_{2}\times100_{2}+1011_{2}\times10_{2}$. This is hardly exciting.

What is $1011_{2}\times100_{2}$? This is almost the same as decimal. The answer is $101100_{2}$. Because binary numbers can only have zeros and ones, there is no need to memorize any multiplication tables.

To return to our example, $1011_{2}\times110_{2}$ eventually becomes $101100_{2}+10110_{2}$, which is then simply added using binary addition.