Numbers and Data
Adding binary numbers
Add two binary numbers place by place, carrying into the next place whenever a column comes to more than one.
Adding in binary works the way adding in ordinary numbers does. You line the two numbers up at their right-hand ends, add one column at a time from right to left, and move anything too big for a column into the column on its left. The only difference is how quickly a column fills up, because binary has just two digits to play with.
When a column overflows
A column can only hold one digit. In ordinary numbers a column overflows once it reaches ten; in binary it overflows as soon as it reaches two, because there is no digit 2 to write down. Whatever a column cannot hold moves one place to the left, where it is worth twice as much. That move is the carry, and it is added into the next column like any other digit.
Worked example
Add the binary numbers 1001 and 101.
Line them up at the right: 1001 above, and 101 sitting under its last three digits.
Lining up at the right is what puts ones under ones and twos under twos. Lining up at the left would add a 4 to a 1.
Try it together
Now work through this one: add the binary numbers 111 and 11.
Take one column at a time, right to left, and say what you write and what you carry.
1.Ones column: 1 and 1. What digit do you write down in that column?
Have a go
Have a go on your own. Add the binary numbers "1010" and "11", and write the answer in binary.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.