#### Adding Binary Numbers

Binary numbers are added the same way as decimal numbers.

The basic rule to remmber is this:

- 0 + 0 = 0
- 1 + 0 = 1
- 1 + 1 = 0 (and carry 1)

As we said before, decimal numbers are based on a deca-system whereas binary number follow a dual system.

Here is an example of a decimal number additon: suppose we want to add then number

**342**to the number**471;****we all know how it's done but let's break it down to investigate:**

- First we add the rightmost digits, and carry forward any digits to the next block

342

+ 471

-------

= 813

- so we added 2 + 1 = 3 then, 4 + 7 = 11 -- write down the digit 1 and carry 1 to the next block (which in fact is the next decade),
- now we add 4 + 3 + 1 and carry over = 8
- write down the final addition as 813 from left to rght

Now let's look at a binary number addition:

Let's say you want to add (010)

_{2}= (2)_{10 }to (110)_{2}= (6)_{10}
The answer shoud be

**(8)10**which in binary is equivalent to the digits**1000**
Let's see:

010

+ 110

------------

1000

This is how it works, step-by-step:

- Starting form the leftmost digit, just like in the decimal system, we add 0 + 0 = 0
- write down 0
- next we add 1+ 1 = 0, write down 0 and carry 1 over t the next binary
- 0 + 1 = 1 + 1 we carried over from before = 0, and carry over 1
- write down 0, carry over and write down 1

The answer written from the leftmost digit is 1000

**(1000)2 = (8)10**