Binary multiplication help

1. Mar 12, 2013

Drao92

How do you multiply 111x111. Every exemple i ve found on internet is 101x100, 110x101 and it doesnt answer to my question :|.
Code (Text):

111x
111=
111+
111+
111
----
Every exemple ive 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 cant understand how this works in binary :|.

2. Mar 12, 2013

SteamKing

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

3. Mar 12, 2013

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 dont understand.

4. Mar 12, 2013

SteamKing

Staff Emeritus
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)

5. Mar 12, 2013

Staff: Mentor

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.