Ever tried—and failed—to understand binary?

Evan if you haven’t, here is the first Shufflenet Tutorial. The topic is: Binary.

### What is binary?

Binary is a number system. The most common number system is base 10. It is the number system that humans use. We use it because we find it easy to use 10s. Just like it’s easy to memorize the 10 times table. Binary is a number system that instead of using 10 different numbers, it only uses 0 and 1. (Bi- means two, for the two different digits—0 and 1.)

Binary is what computers use. They find it easy because there are a very low amount—2—of different digits. Because there are only 2 different digits, this makes the binary number longer. Computer programmers currently can only program computers that use binary. When you use the calculator app on your laptop, it converts the numbers to binary, solves the equation in binary, converts it back to base 10, and displays the answer for you to read.

### How to do basic math in binary

Understanding binary is easy, but different from understanding base 10.

In binary there are four basic rules:

- 0+0=0
- 0+1=1
- 1+0=0
- 1+1=10

But if you want to find out what a number is in binary, this doesn’t help you unless you want to count from 1, all the way up to your number.

### How to find a number in binary

In math class has your teacher ever made you draw a place value chart?

If she has, have you ever noticed that each place value is 10 times the last one?

The first place value is the 0s, then the 10s, followed by the 100s, 1000s, 10000s, you get the idea.

Each place value is 10 times the last one. That’s because you’re using base 10.

Now let’s try doing a binary place chart.

We start by labeling our place values | 16 | 8 | 4 | 2 | 1 |

Now let’s convert a number to binary. Let’s try the number 30. | |||||

30 can be divided into our first place value, 16, once with a remainder. | 1 | ||||

The remainder, 14, can be divided into our second place value 8, once with a remainder. | 1 | 1 | |||

The remainder of that, 6, can be divided into 4, once with a remainder. | 1 | 1 | 1 | ||

The remainder of that, 2, can be divided into 2 once with a remainder | 1 | 1 | 1 | 1 | |

The remainder of that, 0, cannot be divide into 1. | 1 | 1 | 1 | 1 | 0 |

There you have it. 30 in binary is 11110. If you want to check your work, you can add up the place values with a 1 in them. 16+8+4+2=30! I guarantee you it will work every time! | 1 | 1 | 1 | 1 | 0 |

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