Adding binary numbers can be done in much the same way that we add base 10 numbers, with a couple of caveats.

Let’s start at 0₁₀ and add until we reach 4₁₀:

We can see that when adding numbers we need to be very careful when carrying our numbers. This will happen much more frequently than we are used to with decimal numbers. Here are some important rules to remember when adding in binary:

• 1 + 0 = 1
• 1 + 1 = 10
• 1 + 1 + 1 = 11

For larger numbers they can be lined up, one on top of another, just like in the regular addition you are used to. Take a look at the examples below, you can see how often you need to carry in binary addition.

Ex. Adding 100₂ and 1₂:

Binary | Decimal   
       |           
 100   |    4       
+  1   |  + 1       
----   |  ---       
 101   |    5       

Ex. Adding 101101₂ and 111₂:

Binary  | Decimal
  1111  |  1    <- carried digits
 101101 |  45
+   111 | + 7
------- | ---
 110100 |  52