How to add binary numbers together


Binary Addition


To add one binary number to another, you just need to remember 4 rules:

1. 0 + 0 = 0

2. 1 + 0 = 1

3. 1 + 1 = 0 carry 1

4. 1 + 1 + carry 1 = 1 carry 1



Thats it. You should never carry more than 1, if you did then something has gone wrong.

In binary you carry to the left because we start at the least significant number, the far right


For an example we will now add up 101101 and 011000


101101
+011000
----------

Start on the right hand side and add up as normal, referring to rule 1 and 2

As we continue along we see we find a 1 and a 1 needing to be added together

101101
+011000
----------
___101

To continue we refer to rule 3. we add 1 and 1 to make 2. Which is 0 and a carrying 1, so carry the 1 to the left till it finds a 0 to replace

101101
+011000
_1____
----------
__0101


We will represent the carried number in red

We use rule 2 to do the addition

101101
+011000
1_____
----------
_00101


101101
+011000
1______
----------
000101


101101
+011000
----------
1000101

So 101101 plus 011000 equals 1000101