how to add in binary

Question

I don't understand when 100 appear in add what I should do. what the carry for the next step? They are marked with red and blue colors

Answer 1

Let's go step by step:

  000011
  001101
  011011
+ 110110
--------

First we add the values in the 1's column: 1 + 1 + 1 + 0 = 11. We carry the 2's column of the result and continue:

      1
  000011
  001101
  011011
+ 110110
--------
       1

Now we add the values of the 2's column (including the carry): 1 + 1 + 0 + 1 + 1 = 100. I think this is where your confusion started, because the sum has 3 columns instead of 2. We can just carry both extra columns:

    10
  000011
  001101
  011011
+ 110110
--------
      01

Continuing on to add the values of the 4's column: 0 + 0 + 1 + 0 + 1 = 10. We have a 1 to carry over to the 8's column, but there's already a carried 1 there! So we add the two carries: 1 + 1 = 10. Essentially, we shift the carry in the 8's column over the 16's column:

   10
  000011
  001101
  011011
+ 110110
--------
     001

We add the 8's column (0 + 0 + 1 + 1 + 0 = 10) and once again we have a "collision" of our carried values. So just like before, we add the carries, resulting in a "shift":

  10
  000011
  001101
  011011
+ 110110
--------
    0001

Add the 16's column and carries:

  10
   000011
   001101
   011011
+  110110
---------
    00001

After adding the 32's column:

  1
   000011
   001101
   011011
+  110110
---------
   100001

All that remains is our carry in the 64's column:

   000011
   001101
   011011
+  110110
---------
  1100001