OCTAL ADDITION

The octal number system consists of 8 digits ranging from 0 to 7.

So, we add these numbers as we usually would. But there's a slight difference in the process.

5 + 6 = 11. We write 11 below and not write 1 carry 1. Do the same for the other numbers. 7 + 3 = 10. 6 + 4 = 10.

Here's what we do with the 2 digit numbers. We find multiples of 8 ( 0, 8, 16, 24, 32, 40...) closest to the sum. For the first digit , we have 11. The closest would be 8 so we subtract 8 to 11 to get 3. We subtracted it by 8 once so we add 1 to the next digit. 10 + 1 will be 11. Find the multiple closest to 11 which is 8. Perform the subtraction to get 3 and carry 1 to the next digit once again. Repeat the process until all digits are below 8.

The final answer is 1 3 3 3 (Octal).

If we were to do this normally in decimal number system ( 0 - 9) , every time we reach a value of 10 or above, we always carry a 1 and input the remainder. So in octal number system ( 0 - 7) we carry a 1 every time we reach a value of 8 or above. This concept is applied to ANY number system that you can think of.