Multiplication With Signed Numbers

Multiplication technique

To multiply two’s complement numbers we employ the same technique we used in the lesson Multiplication in Binary, with some minor changes.

Before carrying out the multiplication, we sign-extend the number to twice as many bits. This simply means that we add $n$ copies of the sign bit to the left of the number, where $n$ is the number of bits in the original number. For example:

$10001000$ would be sign-extended to $1111111110001000$.

After this, we carry out the multiplication as before. We take the $n$ least-significant bits of the product as our final answer.