Since it is Monday, I won’t ask you to think too much today. Adding binary numbers is actually easier than adding decimal numbers, if you can believe that.

Here’s how to do it. Write 2_{10} binary numbers down, say 1111_{2} and 111_{2}. Make sure to align them on the right, same as you would to add decimal numbers. This should be on your paper/notepad:

1111 + 111

Starting from the right, add the first two digits. 1_{2} + 1_{2} is 10_{2}, so write 0 as the right most digit and carry the 1.

Moving on to the next digit, 1_{2} + 1_{2} + 1_{2}(carried) = 11_{2}, or 3_{10}, so write 1 as the next digit and carry the 1.

Third digit is the exact same. 1_{2} + 1_{2} + 1_{2}(carried) = 11_{2}, or 3_{10}, so write 1 as the next digit and carry the 1.

For the Forth digit, 1_{2} + 1_{2}(carried) is 10_{2}, so write 0 as the right most digit and carry the 1. Drop down the carry, because 1 + 0 is 1 no matter what base you are working with. There’s the answer.

1111 + 111 ----- 10110

Checking the solution is as simple as opening Windows calculator. If you’re not in scientific view, switch to it from the view menu. Select “Bin” for binary mode. Then put in the math problem, same as any other. Now that you know about calculator, try not using it.

Vocab: A digit in binary can be refered to as a bit, so 64-bit, means 64 binary digits.

Homework:

Create 8 or 9 random binary addition problems. If you want to make it hard, write out 64 digits, or bits, for each binary number.