- 2.2 Computers count differently than we do. Introduction to Binary. Your goal in taking this course is to learn how to understand computers better. There is nothing more fundamental to this than binary.

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## Lesson Transcript.

A lot of comments are coming up about binary, hexadecimal, and in general how a computer counts. Now, this will not be the only lesson I do on this subject, but it is an important topic to cover correctly.Go through this slowly, and please ask questions. That is why this is an interactive course.

**Please remember this for all lessons:**

This course is designed so that you can go as slow as you need to. Do not worry about falling behind, or taking too long to finish a lesson. Take as much time as you need to on each lesson. I and others here actively monitor all lessons for questions, and will continue to do so for the duration of the course. Some people may just be starting out, and that is fine. There is no need to rush to "catch up". Take your time.

**How humans count**

When we count, we count in "base ten." Effectively this means we start at 0, then 1, 2, 3, 4, 5, 6, 7, 8, 9 -- and then "ten". Why ten? Well, most likely because we have ten fingers. However, humans also count in base 60 - though you may not have been aware of it until now.

For example, is it 11:58 AM ? That is an example of "base 60." You start at 0, then you keep going until you reach 59. Then you go back to 0. Consider the similarities between:

... 17, 18, 19, 20, 21, 22 ...

and

... 4:57, 4:58, 4:59, 5:00, 5:01 ...

The general rule to remember is this: When one "column" is FULL, the next column over to the left increments by one and the column that becomes full becomes zero. For example:

18, 19, 20 <--- the "ones" column is now full, so it becomes zero. The column next to it (the "tens" column) increments by one to become 2.

**How computers count**

Remember that inside a computer everything is represented as 1s and 0s. A sequence of 1s and 0s is actually a number, the same as: 1,274 is a number. In base ten, a column is full once it reaches 9. In base 60 a column is full once it reaches 59. Well, in base 2 (binary, 1s and 0s), a column is full once it reaches ONE.

So, you start counting like this: 0, 1

Ok, what now?

Well, like we talked about - the column is now full. It is full because it contains the highest allowed number, in this case a 1. Therefore, the "full" column must now become zero, and the column over to the left must now increase. Since at present that column is empty, it must become a 1. So:

00, 01, 10

ten? No. Two. Don't be confused. 10 all your life has meant "ten", but I want you to think of it as meaning something different: Two columns, and a value in each one.

Lets talk about the number 35 (thirty-five). It really means: 3 in the tens column, and five in the ones column. Each column in base-10 as you move over to the left becomes ten times the previous. So you go: ones, tens, hundreds, thousands, etc.

In base 2 (binary), each column doubles from the previous, so you go: 1, 2, 4, 8, 16, etc.

Here is a graphic that helps to illustrate this:

For example, the binary number: 0100 means this: You have a 0 in the ones place, a 0 in the twos place, and a 1 in the fours place, and a 0 in the eights place. Therefore, the number is "four".

So lets go back to counting in binary:

0, 1, 10 (because once a column is full, we go to the next column) then: 11 (three), 100 (four), 101 (five), 110 (six), 111 (seven).

Now, what do we do next? What would we do if the number was nine-hundred and ninety-nine? 999 ? Watch:

999 + 1

1000

Three columns are full, we go to the next one to the left. Now binary:

111 + 1

1000 A thousand? No - eight. There is a one in the eights place, a 0 in the fours, a 0 in the twos and a 0 in the one's place.

It is very important that everyone masters this. Please feel free to ask any questions.

In addition, optional supplemental videos on binary have been added. Keep in mind these videos are entirely optional offered for those who wish to expand their understanding of binary.

**You do not need to watch these videos to complete the course.**Be sure you have finished this lesson (including watching the video version of this lesson that is linked at the top) before watching the below videos.

How to add binary numbers

How to subtract binary numbers

How to multiply binary numbers

How to divide binary numbers

### When you have finished this lesson, proceed to:

- 2.3 Patterns and Place Values of Binary In this lesson I will show you how binary produces patterns that make it simpler to understand. You will find that starting at zero and counting in binary is quite easy.