Binary Addition

We talked about what binary is in the previous section, but making use of these numbers through binary addition allows the computer system to perform more complex tasks.

binary numbers

Adding binary digits together requires a set of simple rules that you likely learnt in primary school:

0 + 0 = 0

0 + 1 = 1

1 + 1 = 10   (2 in binary)

1 + 1 + 1 = 11   (3 in binary)

The process of adding binary numbers together requires you to use the same process as long addition in maths. Each time a number becomes more than one digit long, the digit is carried over to the next column.

This can be seen when adding the numbers 10 and 5 together.

First, convert both denary numbers to binary:

Binary table showing bit pattern for 10 and 5

Now we can apply the rules of binary addition to each column from right to left. In this case, there are no columns that require us to carry any digits:

Table showing binary addition of 10 and 5

We can see here that once the rules have been applied, the resulting number adds up to the denary addition of the two numbers. We can check this by converting the result back to denary.

So what does it look like with a more complex calculation? Let’s try adding 7 and 12:

Table showing binary addition for 7 and 12 - highlighs the carried digits

Notice that this time we have carried the 1 to the left where the rules state the answer is 10. This carried digit is then added as part of the next column.

Try It For Yourself!

Click the Refresh button to generate your binary calculation.

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