Can I teach you to do math in binary in 20 minutes?

Adding numbers in binary is a lot simpler than you might think. Follow along and learn how it's done.

Note: I will mark all binary numbers in red, and regular decimal numbers in blue.

Let's try an example

Imagine we want to calculate 3 + 1. In binary, they are 11, and 1 respectively.

   1 1    <--- start from the right
+ 0 1
------

We start from the right, by adding 1 + 1, which is 2 in decimal. In binary, it's written as 10.

But when we are adding in binary, we can only add single digits, 0 or 1. So we need to carry the 1, and add the 0.

   1  <--- carry the one
   1 1
+ 0 1
------
      0  <--- add the zero

Now we move on to the next number.

Carried from the previous 10's
  ↓ ↓
   1 1
      1 1
+    0 1
--------
   1 0 0

We calculate the carry with the next line, 1 + 1 + 0. But that also gives 10, so we need to carry it again, and put 0 as the sum at the bottom.

And if we add the last 1 to the bottom, we have 100.

That's it. You've calculated 3 + 1 in binary. Try it yourself by hand with a different number! At the bottom of this page there is a handy generator for testing if you got it right. :)

The logic types

If you're interested in building the logic yourself in code, here's how to do it. There are only 3 types needed.

XOR

Takes two inputs, A and B. If they're different from each other, output is 1, otherwise 0.

XOR(0, 0) == 0
XOR(0, 1) == 1
XOR(1, 0) == 1
XOR(1, 1) == 0

In JavaScript:

function XOR(a, b) {
    if (a !== b) {
        return 1;
    } else {
        return 0;
    }
}

AND

Takes two inputs, A and B. If they're both 1, it will output 1, otherwise 0.

AND(0, 0) == 0
AND(0, 1) == 0
AND(1, 0) == 0
AND(1, 1) == 1

In JavaScript:

function AND(a, b) {
    if (a == 1 && b == 1) {
        return 1;
    } else {
        return 0;
}

OR

Takes two inputs, A and B. If either or both are 1, it will output 1, otherwise 0.

OR(0, 0) == 0
OR(0, 1) == 1
OR(1, 0) == 1
OR(1, 1) == 1

In JavaScript:

function OR(a, b) {
    if (a == 1 || b == 1) {
        return 1;
    } else {
        return 0;
    }
}

These logic types can be implemented in hardware with the help of transistors and resistors, but it's easier in code.

Here is the logic chart for adding numbers in binary:

Here, A and B are our two numbers we want to add, and C is a carried number if the number is longer than one digit. The Carry out leads into an identical chart, because you need to run it on every digit in your two numbers, starting from the back.

Using the functions we defined earlier, XOR, AND, OR, and chaining them together according to the chart, you can add numbers in binary. Test different numbers for yourself below.

Number 1                        Binary
Number 2                        Binary
Equals                              Binary