# Multiplication of Binary Numbers

A tutorial on how to multiply binary numbers, along with examples, exercises and answers is presented.

## Add binary numbers with one digit

let us first add binary numbers with one digit.
0 x 0 = 0
0 x 1 = 1
1 x 0 = 1
1 x 1 = 1
The above simple mutliplications are similar to those of decimal.

## Multiply binary numbers

We now multiply numbers with more than one digit: 1 0 1 1 x 1 0 0 1

The multiplication of binary numbers is similar to the multiplication of decimal numbers.

 1 0 1 1 x 1 0 0 1 ____ ____ ____ ____ 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 ___ ___ ___ ___ ___ ___ ___ 1 1 0 0 0 1 1

The multiplication of binary numbers is done by shifting by one bit and adding. It can be easily checked that 1011 which is 11 in decimal multiplied by 1001 which is 9 in binary gives 99 which is 1100011 in binary.

## Exercises

A) Multiply the binary numbers.
1. 111 x 11
2. 1011 x 111
3. 10101 x 1101
4. 100011 x 1100011 (you need to know that 1 + 1 + 1 + 1 = 100 carry 10)