Exploring Computer Hardware

Binary Multiplication

Multiplying binary numbers together is fairly straight forward. All you have to remember are these simple rules...

0 x 0 = 0

0 x 1 = 0

1 x 0 = 0

1 x 1 = 1

Lets try an example. Multiply 101 x 11

First we multiply 101 by the first 1, following the rules above.

101

11 x

101

Then on the next line, we put a 0 as a place-holder

101

11 x

101

0 <-- add place-holder

Then multiply 101 by second 1, which produces 101.

101

11 x

101

1010 +

Once you’ve done the that, add the two together (101 + 1010) using the binary addition rules.

101

11 x

101

1010 +

1111

So 101 x 11 = 1111

(in decimal 5 x 3 = 15)