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In order to talk to machines, you have to speak in their language. Machine language is usually represented in binary form. Binary is a numbering system that only uses the digits 0 and 1. When these numbers, 0 and 1 are arranged correctly they represent everything we do on the computer.

Binary Number Game (music begins automatically)

Unlike Decimals which use 10 as a base, Binary numbers are figured by multiples of 2.

Here's a mathematical tip for understanding Binary:

What is `101011`

?

```
1 x 1 = 1
```

1 x 2 = 2

0 x 4 = 0

1 x 8 = 8

0 x 16 = 0

1 x 32 = 32

1 + 2 + 8 + 32 = 43

In order to talk to machines, you have to speak in their language. 0:00 Early on, we figured out ways to extract code from machine languages. 0:04 But, in order to step forward, 0:08 we must step down to some lower level machine code. 0:09 The binary numbering system is similar to the decimal numbering system you're 0:12 already use to in many ways. 0:16 The principles behind the systems are similar, but 0:18 obviously there's some differences as well. 0:21 Let's start with some names you may already be familiar with. 0:24 A bit is the smallest unit in binary, and it can either be a zero or a one. 0:27 If you put eight bits together it's a byte. 0:33 Both the decimal and binary numbering system, are positional numbering systems 0:36 meaning, the position of the numbers indicate the relative value. 0:41 Let's look at an example. 0:45 In the number 1,234, the 1 is worth 1000, 0:47 the 2 is worth 200, the 3 is worth 30 and the 4 is worth 4. 0:52 If you switch these numbers around, their relative values will also switch around. 0:58 The decimal system accomplishes this place value by using 10 as the base, and 1:04 increasing the power each time you step to the left, or 10 the 0, 10 to the 1, 1:10 10 to the 2, are the ones, tens, and hundreds place. 1:14 This same process happens in binary. 1:19 Only it uses two as the base instead of ten so the first position is two to zero 1:22 the second position is two the first, the third position is two to the second and 1:27 the fourth position is two to the third, representing the ones, 1:33 twos, fours and eights place. 1:37 Now, let's use our knowledge of place value to find out 1:41 what this bite represents. 1:44 Don't be shy, take a guess. 1:46 [SOUND] That's right, it's 1. 1:48 Here we've turned on the first bit which represents a 1 or 1:51 a 0 meaning this equals 1. 1:56 Let's try another, what about this bite? 2:01 Here we've turned on the second bit which represents two, so this bit equals two. 2:04 And, what about this one? 2:12 Here we've turned on the first two bits, the two and 2:14 the one, because two and one equals three. 2:17 This represents three. 2:21 [BLANK_AUDIO] 2:22 Let's skip ahead a little bit. 2:25 What do you think this byte will represent? 2:27 Here we have the 8 and 2:30 the 2 bits turned on, so this represent 10, because 8 plus 2 is 10. 2:31 Now, let me assure you none of the languages we teach here at 2:37 Treehouse use the binary numbering system. 2:41 But, it's important to know where your data is going, and 2:44 what it looks like to a computer. 2:46 In the next video, 2:49 we'll look at a laptop tear down to see what data storage hardware looks like. 2:50

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