Multiply binary numbers - how it works

Often you convert binary numbers into decimal numbers before you want to multiply them. But there is a faster way: In this practical tip you will learn how you can easily multiply binary numbers yourself.

How to multiply each binary number

• Multiplying binary numbers together sounds very complicated. But it is not at all. Computing in the dual system is just as easy as in the decimal system. Here, however, there are not ten occurrences of a digit, but only two (0 and 1).
• The rules of multiplication are exactly the same. Factor times factor equals product. If you want to calculate the result of two numbers manually, then write both next to each other and leave some space downwards (example in the next paragraph). Now multiply each digit individually by each, whereby the following applies:
• 0 times 0 equals 0
• 0 times 1 equals 0
• 1 times 0 equals 0
• 1 times 1 equals 1
• Add all the numbers together and you get the final result. But it can happen that one or the other "2" has cheated into the solution. A binary number from the dual system may only consist of 0 and 1. What should you do with it?
• So if you get a 2 at any point, it is equivalent to a 0. However, the 2 also affects the next digit on the left. This is then reversed. A 1 becomes 0 and a 0 becomes 1. Mathematically, an additional 1 is added to the next position, which causes this reversal.

Multiply binary numbers - example

• In this example, the binary number of 10 (1010) is multiplied by the binary number of 11 (1011). The solution to this equation should be 110 (1101110).
• 1010 is therefore calculated with a single digit of 1011 times. As with multiplication in the decimal system, make sure that you move one digit to the right after each digit.
• These 4 intermediate results are added together in the usual way and you get the value 1021110 in this case. You can see that the result contains a 2 which the dual system cannot process. The 2 is converted into a 0 and the next digit gets a 1.
• So the new result 1101110 is calculated that only consists of our two binary numbers - and we see the solution is correct.

On the next page you will find instructions on how you can easily convert binary numbers to decimal numbers.