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