Binary Arithmetic 1

Addition of binary numbers is based around how it is done when adding two numbers using pen and paper. In decimal form, 1 + 0 = 1, 0 + 1 = 1, and 1 + 1 = 2. This is the same as binary... but remember that 2 isn't a binary number? So, the correct way to do it is, 1 + 1 = 10. Similarly enough, 1 + 1 + 1 = 11. Lets look at the addition of the numbers 14 and 23 which are 1110 and 10111 respectively.

As can be seen here, it works out. When your adding two binary digits, e.g. 1 + 0, you get 1 as discussed before. When you add 1 + 1, you get 10, but the way to do this is to write down the 0 underneath, and carry the 1 on to the next set of digits.

As can be seen on the column second from right, a 0 is written under the two 1's. Here, the answer is 10, but the 0 is written, and the 1 is carried over to the next two 1's. Here, this is 1 + 1 + 1 = 11, but is written here, 1 goes underneath and 1 is carried over to the 1 and 0, etc.

This method works for adding two positive numbers. One thing to note is that we haven't come across any negative form of numbers yet, but it will be dealt with soon. To help with any problems with addition, you can study these addition questions and solutions to make sure you can get it right.

1 0 1 1 0 1	1 0 0 0 1 0	1 1 0 1 1 1	1 0 0 1 1 0 1 1	1 0 1 1
1 1 1 0 1 0	1 0	1 0 1 1 1 0 0 1	1 0 1 0 0 0 0	1 0 1 1
1 1 0 0 1 1 1	1 0 0 1 0 0	1 1 1 1 0 0 0 0	1 1 1 0 1 0 1 1	1 0 1 1 0