How to multiply binary numbers together


Binary Multiplication


To multiply one binary number to another, there are 2 steps:

Step 1: Multiplication

To multiply one binary number to another, you just need to remember 2 rules:

1. Only 1 x 1 = 1

2. 1 + 0 = 1

2. With each multiplication you shift the value along by 1



Thats it. 2 Rules gets you through the first step.


101
x 110
----------

Start on the right hand side and multiply up as normal, referring to rule 1

Start by multiplying the bottom right hand value with each of the top values starting on the left.

101
x 110
----------

As the value is 0 every value will be nothing, so we will ignore this and skip to the next to the left. But I will leave in the 0s to keep the reference there.

101
x 110
----------
000
1010

As you see by following both rules above we get the value 1010 instead of 101 only because rule 2 means because we are on the 2nd value from the left on the bottom number, there is a value to its right, which was the 0. Regardless if this is a 0 or not, we have to shift the value along by 1 by adding a 0 to the end.

101
x 110
----------
000
1010
10100


Seen as the final number had 2 values to the left, we shift the value 2 places to the left with 0s.

This is the end of Step 1. Step 2 is addition, we need to now add the values gained from the multiplication together.

Step 2: Addition

You can either follow on from here or use the same way as on the Binary Addition page: Binary Addition

To add one binary number to another, you just need to remember 4 rules:

1. 0 + 0 = 0

2. 1 + 0 = 1

3. 1 + 1 = 0 carry 1

4. 1 + 1 + carry 1 = 1 carry 1



Thats it. You should never carry more than 1, if you did then something has gone wrong.

In binary you carry to the left because we start at the least significant number, the far right

Below are our values gained from the multiplication.

000
1010
10100

Seen as the top row is all 0s we will just ignore it entirely.

1010
10100
-----
11110

We are simply adding 1 to 0 with the exception of the right hand side which was 0 + 0.

So 101 multiplied by 110 equals 11110