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Binary numbers are the basis for all that is happening inside computers or electronic devices. In this lesson, learn how to multiply and divide binary numbers.
Binary Multiplication
Binary division and multiplication are both pretty easy operations. Instead of dealing with a lot of numbers, you just need to make sure to set the 1 or 0 in the right place. For this reason, you need to make sure you are also familiar with binary addition and subtraction.
To perform a binary multiplication problem, we need to understand how addition works with binary numbers and follow the same process of multiplication and addition we would use with decimal numbers.
Let’s say we want to multiply 4 by 3, which in binary will be 100 by 011 (or 11, it’s the same):
4 x 3
Binary Multiplication
We start with the first digit, in this case 1, and multiply 100 by 1, which gives the exact same number.
1 multiplied by 100
First digit multiplication
Then we move to the second digit and proceed to do the same. Since it’s also 1, the number will remain intact, we just need to shift the number one digit to the left:
Second digit multiplication shifts one digit
Second digit multiplication
Later, since the last digit is a 0, we can skip it and start with the addition:
Skip the 0 and start adding
Ready to start adding
0 added to 0 is 0. And, 1 added to 0 is 1:
Final result of 4 x 3
Final result
We can verify that the result is 12 by converting the binary product to decimal.
Now, let’s try with a harder example. Let’s multiply 12 by 15, which in binary will be 1100 by 1111.
12 x 15
Multiplication structure
First, you take the first digit from 1111 and multiply it by 1100, which gives the same number:
1100 multiplied by the first digit
First digit multiplication
Now we’re going to repeat the same process with each digit, shifting to the left with each of them, getting this descending series of 1100s:
Products ready to be added
All the digits multiplied
Finally, we just need to add the numbers. This can be a little tricky when you add several 1’s in a row.
Once we reach the column with the two consecutive 1’s, remember that the result is 0 and we carry a 1 to the next column.
Add two 1s, carry a 1 to the next column
Adding all the products
In the next column, we need to add the numbers by pairs. The first two 1’s will add up to 0, carry a 1, then, the result 0 plus the 1 will add up to 1.
Keep track of the result of each individual addition
Adding all the products
We keep repeating the same process until we finish all the addition:
The result is 180
Final result
We can check that 12 multiplied by 15 is 180, which in binary is 10110100.
Binary Division
To perform a binary division, we need to follow the same process as we do for dividing regular numbers but, in this case, we only need to decide if it’s going to be a 1 or a 0.
To divide two numbers, which result is an exact division, we basically need to follow four steps: division, multiplication, subtraction, and next digit.
Let’s say that we want to divide 18 by 3, which in binary will be 10010 divided by 00011 (or 11, it’s the same).
18 / 3
Initinal structure of division
First, we need to identify digit by digit. Is 11 less or equal than 1? No, so we get another digit. Is 11 less or equal than 10? No, so we repeat and get another digit. Is 11 less or equal than 100? Yes, so in this case we don’t need to think how many times can 100 be divided by 11, instead, we just add a 1 to the product.
100 can be divided by 11
Initial division identification
 
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