4th July 2008

Binary Numbers (Part 3) - Multiplying & Dividing binary numbers

In this third part we will show you how to multiply and divide binary values.

In part three:

Multiplying binary numbers

Binary multiplication can be achieved in a similar fashion to multiplying decimal values.

Using the long multiplication method, ie, by multiplying each digit in turn, and then adding the values together.

For example, lets do the following multiplication: 1011 x 111 (decimal 11₁₀ x 7₁₀)
binary multiplication

which gives us 1001101, now we can convert this value into decimal, which gives 77₁₀

So the full calculation in decimal is 11₁₀ x 7₁₀ = 77₁₀ (correct !!)

note: Notice the pattern in the partial products, as you can see multiplying a binary value by two can be achieved by shifting the bits to the left and adding zeroes to the right.

Dividing binary numbers

Like multiplication, dividing binary values is the same as long division in decimal.

For example, lets do the following division: 1001 ÷ 11 (decimal 9₁₀ ÷ 3₁₀)
binary multiplication

which gives us 0011, now we can convert this value into decimal, which gives 3₁₀

So the full calculation in decimal is 9₁₀ ÷ 3₁₀ = 3₁₀ (correct !!)

note: Dividing a binary value by two can also be achieved by shifting the bits to the right and adding zeroes to the left.