Binary Addition and Carrying: How to Multiply 111x111

[Drao92]

How do you multiply 111x111. Every exemple i ve found on internet is 101x100, 110x101 and it doesn't answer to my question :|.

         111x
         111=
         111+
        111+
       111
       ----
Every exemple I've found is like :))
  110+
  101
   
Which is obviously easy...

The problem i have is the summing of 111+111+111, when i get 1+1+1=? I can't understand how this works in binary :|.

 

[SteamKing]

If you have 9+9+9 in decimal, how does that work?

 

[Drao92]

i keep the first digit and i add it with the next digits.
But if i have to sum 1+1+1 in the sum coulm This is (1+1+1+1)=(10+1+1)=100, what i do here, i keep the last digit and i add 10 to the next sum, this is what i don't understand.

 

[SteamKing]

It's probably easier to see what to do if you add two binary numbers at a time.

If you have (binary) 111 + 111, then, starting from the rightmost column,

1+1 = 10, write down 0, carry 1 back to the next column to the left
1+1+1 = 11, write down 1,carry 1 back to the next column to the left
1+1+1 = 11, the sum becomes

11 1 0 is the final result

check, 7+7 = 14 (decimal)

 

[Mark44]

To back up a bit from what SteamKing said, there are four addition facts that come into play.
1. 0 + 0 = 0
2. 0 + 1 = 1
3. 1 + 0 = 1
4. 1 + 1 = 10
The only one of these that deserves discussion is the last: 1 + 1 = 0, and you carry 1 to the next higher place.