Over the years I’ve been asked to explain this to many people and most of the times as I was done explaining this, people would say “Huh, I thought it was harder!”. I think the reason is that when people are taught how to do this they are shown the math behind it and they immediately get bored and switch to “don’t know, don’t care” mode. I’m not going to go over the math behind binary numbers because you can look that up anywhere but I’m going to show you a quick and dirty way that works every time.

*The fact is, you can learn how to read and write binary numbers just by doing simple additions.*

First of all, let’s build our mental cheat sheet. You will be writing a sequence of numbers starting from 1. The next number in the sequence will be the previous one times two. You will put each successive number to the *left* of the previous one. If you didn’t understand the previous two sentences don’t bother reading them back, just look at the picture and see if you can deduce the sequence because this is as hard as it gets. The rest is downhill:

As you can see, if you take any number in the sequence and double it you get the number to the left. If you half your number, you get the number to your right.

Now write your binary number on top of your cheat sheet. Let’s take the number 10111 and write it on your cheat sheet. It’s OK if you have extra numbers on your cheat sheet, you can just leave them blank as we are not going to use them.

Now you add whatever numbers you have under every 1 and discard the numbers under every 0. Like this:

It’s *that* simple.

Here are some other few examples if you want to try this out for yourself.

- 11
- 1001
- 10010
- 10000011

(Click the spoiler alert to show the answers)

Answers:

1) 3

2) 9

3) 18

4) 131