Binary multiplication uses the same technique as decimal multiplication. In fact, binary multiplication is much easier because each digit we multiply by is either zero or one. Consider the simple problem of multiplying 1102 by 102. We can use this problem to review some terminology and illustrate the rules for binary multiplication.

 First, we note that 1102 is our multiplicand and 102 is our multiplier. ``` 110 x 10``` We begin by multiplying 1102 by the rightmost digit of our multiplier which is 0. Any number times zero is zero, so we just write zeros below. ``` 110 x 10 000``` Now we multiply the multiplicand by the next digit of our multiplier which is 1. To perform this multiplication, we just need to copy the multiplicand and shift it one column to the left as we do in decimal multiplication. ``` 110 x 10 000 110``` Now we add our results together. The product of our multiplication is 11002. ``` 110 x 10 000 110 1100```

When performing binary multiplication, remember the following rules:

1. Copy the multiplicand when the multiplier digit is 1. Otherwise, write a row of zeros.
1. Shift your results one column to the left as you move to a new multiplier digit.
1. Add the results together using binary addition to find the product.

The animation below shows how to multiply the binary numbers 11112 and 10112. Click on the "Start Tutorial" button to view the animation.

Text-only version