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Omg you are a legand what a fantastic no confusing way of explaining thank you a million 🙂

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- Understanding the Binary System

**The secret of the binary system?**

The first thing to know is that you read binary numbers from right to left. The second thing you need to understand is that each digit is based on a power of the number 2. Check this out:

2 to the power of 0 equals 1

2 to the power of 1 equals 2

2 to the power of 2 equals 4

2 to the power of 3 equals 8

2 to the power of 4 equals 16

2 to the power of 5 equals 32

2 to the power of 6 equals 64

2 to the power of 7 equals 128

…

See the pattern? Now let’s take these numbers to use them as a template while remembering that binary numbers are read from right to left:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

Now let’s use this template on that ugly binary number from our earlier example. At the top is our template, at the bottom is our binary number:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 |

Now we use simple multiplication and addition. If the binary number is a 1, it means this digit is “on” or “true” and we add the corresponding number from the template, if it is a 0, it means the digit is “off” or “false”, and we do not add the corresponding number from the template.

In our example, the digits for 128, 32, 8, 4 and 2 are true, so we add

128 + 32 + 8 + 4 + 2 = 174

You could also express it as

128*1 + 64*0 + 32*1 + 16*0 + 8*1 + 4*1 + 2*1 + 1*0 = 174

This means our binary number 10101110 is the number 174 in the decimal system.

Page 1: What is the binary system

Page 2: This page

Page 3: Bits vs bytes, some terminology

Page 4: Bus width

Sam says

Omg you are a legand what a fantastic no confusing way of explaining thank you a million 🙂

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