# Binary – How to Make a Computer: Part II

The number 10 is everywhere. Cultures around the world give multiples and
powers of ten a kind of special significance. 10 is so central to our collective understanding
of mathematics, that it’s possible you’ve never even questioned its primacy – But
basing a number system around 10 is actually pretty arbitrary: we have ten fingers, after
all, so it’s only natural that our counting system would be based on the number 10. Our system of writing numbers is called Base
Ten or Decimal. Today, this system of counting is so ubiquitous
that we rarely stop to think about why we write numbers the way we do. But there are other ways of counting, based
around other numbers than ten. In this episode, we’ll briefly be getting
our head around some of these by learning Octal (base-8) and Quaternary (base-4) before
moving on to Binary (Base-2), the number system that computers use to count. By the end of this episode, you’ll know
how, and more importantly why computers perform complex mathematics with just two digits:
one, and zero. Our number system, the Hindu-Arabic number
system, does not have a single symbol for 10, instead, the number is made of 2 digits,
which signify 1 ten and 0 ones. Any number is made up of digits, and each
different digit corresponds to a different power of 10. 4675, for example, is equal to four times
one thousand, plus six times one hundred, plus seven times ten, plus five times one. Which is equal to four times ten to the power
of three, plus six times ten to the power of two, plus seven times ten to the power
of one, plus five times ten to the power of zero. This is a counter – specifically a base-10,
or Decimal counter. It’s the kind of counter you’ve encountered
your whole life, so this should look pretty familiar to you. Right now we’re just counting up from zero
– after reaching the number 9, we have no more digits left for the ones’ position,
so it rolls back over to zero, and the next position increases by one. As I mentioned before, the reason we use base
10 can be attributed to the fact that we have 10 fingers. It makes sense that we’d base our counting
around a number that we can intuitively understand. So what if you grew up in a society with 8
fingers instead of 10? Base-8, or Octal, is a number system with
just 8 digits: 0, 1, 2, 3, 4, 5, 6, 7 Counting up one digit at a time, once we get
to 7 in this system, we have no more digits left for the first position, so it rolls back
to 0 and the second position is increased by 1, just like in base 10. This number, 1-0 in Base-8, is not “Ten”
as we know it. As we can see, the counter still only advanced
by eight positions in total, meaning that 1-0 in base-8 is equal to the number eight. This position is therefore, clearly equal
to the number of eights in the number. This reads: 1 Eight, plus 0 Ones. Clearly, in Base-8, the positions correspond
to different numbers than what we’re used to in Base-10. So what are they? Just like how in Base-10, the positions correspond
to powers of 10, the positions correspond to powers of 8 in Base-8. The first column is the number of ones (8^0=1) The second column is the number of eights
(8^1=8) The third column is the number of sixty-fours
(8^2=64) The fourth column is the number of five hundred-twelves
(8^3=512) And so on. This might seem like a very alien and foreign
way to write numbers, but it’s just as valid as decimal in every way – you’re just not
used to doing it this way. Now that have a better understanding of how
base-10 and base-8 work, you might already have some ideas of how base-4 works. Base 4 has 4 numerals – 0, 1, 2, and 3. Each position is based on powers of 4:
The first position is the ones position (4^0) The second position is the fours position
(4^1) The third position is the sixteens position
(4^2) The fourth position is the sixty-fours position
(4^3) And so on. Counting up from 0 again, in Base-4 you can
see how quickly each column fills up – it only takes sixteen counts to get up to 4-digit
numbers. But remember, even though this number looks
like 100, it’s still equal to just 16 in base-10. Just keep thinking of numbers as being made
up of individual digits multiplied by their positions. Now, we’ve got to Base-2, or Binary. Binary about as uncomplex as a positional
number system can get. It has just 2 numerals, 1 and 0. The positions are based on powers of 2. First is 2^0, the number of ones. Second is 2^1, the number of twos. Then 2^2, the number of fours. Then 2^3, the number of Eights. Then 2^4, the number of sixteens. Then 2^5, the number of thirty-twos. Then 2^6, the number of sixty-fours. Then 2^7, one hundred and twenty-eight. With 8 positions, binary can display numbers
up to 255. Counting up from zero, you can see that the
positions on the counter fill up very quickly – after a position reaches one, there are
no more digits left, so it ticks over to zero and adds one to the next position. Since each position can only have a 1 or a
0 in it, each position in a binary number can be abstracted to be equal to one of two
states, on, or off, yes, or no. As you may recall from the last episodes,
the electronic components of logic gates could also be equal to only two states – powered
or unpowered. For this reason, binary has become the go-to
way of manipulating numbers using electronic circuits. A binary number can just as easily be represented
by lightbulbs, switches or a set of currents than it can be by numbers. A binary digit, or bit, is the smallest unit
of information possible – a boolean – true or false – yes or no. Next episode, you’ll expand your knowledge
of binary. You’ll learn how to add binary numbers,
both manually and with electronic logic circuits. In no time, you’ll know just how to arrange
simple wires, switches and relays to add two numbers together automatically.

## 100 thoughts to “Binary – How to Make a Computer: Part II”

1. the skeleton posse says:

your videos are the fucking bomb. also, this series is fantastic.

2. Ares noname says:

Hm, it seems too much time to explain a pretty basic thing. Still the series so far

3. GamingNinjaSheep says:

I'm studying automation engineering and basically know all this by heart but for some reason it's still really interesting to watch, it sort of refreshes my memory. Keep it up!

4. Dinuka Jay Vlogs says:

Worth the wait as always. Good stuff Josh!

5. Andreas Sihm says:

DOPE

6. ㅤㅤ says:

Great video, really liking this series

7. Alex Stedman says:

Great video m8!

8. Anuel says:

Good job!

9. Termination Shock says:

Man, I'm following you since your first two videos. I thought they were good but now I truly understand that you deserve your 10.000 subscribers and many more. Keep up the great work!

10. AlphaOmega says:

Really nice job on this man

11. Tomas Beblar says:

Can't wait for video 3 of "How to build a computer. I'm a software dev with 10+ years of experience and these videos are a great refresher for me as well as a how to guide I can send to friends interested in the topic. This channel has potential. Keep it up!

12. ColumboJedi says:

You are the person I would like to be. Thank you for this content very much !!

13. Alec Bertoy says:

The editing is so snazzy in these videos I love it. Can't wait to see the rest of the series!

14. Richard Hazinski says:

Not sure if I should hyped about your next video about mars since I love space or sad because I have to wait longer to get the next computer video.

15. Jack DuVal says:

Cool vid!

16. elliotsoomro says:

This is literary the best series on youtube!

17. Niboe says:

I was waiting for you to get to something I didn't know, but I'll have to wait until next episode for that I guess.
I gotta remember that not everyone is familiar with binary! Even the least mathy person could understand your explanation of binary

18. Zane Brainard says:

Great video. How fast are you going to make these?

19. Desert Fox says:

Great work, can't wait for the next video, and hope to see more video series like this one in the future, also hoping to see some astronomy videos from u soon

20. Green Stone Boy says:

do more pls ♥

21. xMack says:

Amazing video, hope your channel will grow fast 😀
Also, very much looking forward to the next video

22. MeTube says:

My mind is officially blown! Respect! You're a master teacher.

23. A Miller says:

Wow, you're like CGP Grey but you actually know how to do art

24. Matthew Wright says:

great video!

25. Rohan Dvivedi says:

waiting for next video in this series

26. Marco L says:

Is it correct to say the term base 10 could mean any number system? The only reason base 10 means decimal to use is cause we use it as our main system. Like for example is someone used a base 8 number system they would call it base 10.

27. Mortizul says:

Brilliant. Keep going. You have a talent for this.

28. Aiden says:

I love you.

you, CPGgrey, Wendover productions, and that criwkwnd in a nutshell guy

If only someone had showed me this video when I was in 9th grade messing up over 0s and 1s

30. Almond Heng says:

Hello Josh. It seems that you haven't added this video into the How To Make a Computer series playlist. I would definitely appreciate if you add this and the coming videos too because I would constantly check the playlist to follow up with your new (and awesome) videos. A big thanks from your fan! 😀

31. The Leeds Project says:

32. Gopi Krishna says:

Simply awesome 👌👌👌 can't wait for the next…

34. Dean McKenzie says:

Again, Petzold drags this out a bit, but the animation of the "counters" was genius.

35. SuperAnthony1982 says:

Even though I already know all this stuff intrinsically I still enjoyed watching..i wish I had something like this while I was learning, somehow you get everything across in a way that other sources just can't I am going to use these to teach my kids! really great stuff!

36. Martin Tirpák says:

you deserve hundreds of thousands of subs and millions of views. If I was able to see this video when I was younger and learning binary, it would boost me by miles.. Keep up the high quality!

37. Patrick Ventur says:

Great, never get how it works until now! Please go on 🙂

38. Phrenomythic says:

Very well explained and illustrated!

39. Rudy_Eila says:

Are you going to continue this series? It's very well done so far.

40. Bnani Blaoi says:

Keep up the great work!
Can't wait for the next video!

41. gorillaau says:

There are 10 types of people in the world. Those that understand binary and those that don't.

42. Cristopher González Vega says:

Great video bro

43. Mawesome4ever says:

Please make a Part 3 ;/

44. 10,000 subs no videos challenge says:

Thanks so much this is really informative. Please continue making this series.

I still waiting that next video

46. Tuff Nerd says:

en-counter wow great job there

* slow clap *

47. Matthew Swanson says:

when 3rd episode will be released?

49. VIIflegias says:

such neat ang tidy explanations, easy to understand. can't wait for the next video, sensei!

p.s. i know simplifying things can be hard, so if you need to step up the difficulty a bit, i think we can handle it.

50. Tom Wheater says:

Is there going to be a 3rd video?

51. Tytanium says:

Holy shit highest quality videos I've seen in a while…
This channel is under rated.

52. isuru srimal says:

grate video.. simple to understand.. please release the next video… good luck..

53. BKBrunelle74 says:

I went looking for video 3 of this series and it's not there. Are you going to finish this series?

54. Satvik Soni says:

Why don't schools teach like this 🙁

Hey, just wondering if you gave up on this. I know all this stuff already but I really enjoy the way you present it 😉

56. Redwolf Plays says:

1:53 It's kind of counter you've en counter ed😂

57. Matthew Pollock says:

Dude, a few years ago I had to go from no understanding of electricity and electronics to… well, I'm still not an expert, but I do have an A&P. I gotta tell you, videos like these would have done wonders for me. So looking forward to the next video!

58. Deliquescator says:

This is amazing! I've learnt binary in College but this way it makes so much sense!

59. Floris Bollen says:

Nice video!, You explain it very clearly! Can't wait for the next video!

60. lego technic says:

Why did this channel die?
No videos since 7 months!

61. Parth Gohil says:

I wish you completed the series.
I landed on your channel and immediately subscribed and turned on notifications from wendover production video.
This may be one of those series that anyone would create a patreon account for.

62. WASIM FIROZ KHAN says:

waiting for next part!

63. Alexander Vezina says:

We want more! #bestvideosever

64. Willisburg says:

Wow, this is really awesome interesting, and well presented, but when will the 3rd video will be released?

65. Mauro Ferreira says:

Really lovely work ou explain so simply!! When the part 3 comes?

66. Herbalninja says:

I hope you post part 3 soon 🙂

hey I really appreciate your work. I want part 3

68. aman bhandari says:

Please make more videos on this topic

69. Error Rty says:

Cant wait for part 3 you're really awesome

70. tbone912 says:

Dude, this would have been an awesome series. You'd probably explain the complicated parts well.

71. Marcos Beffa says:

rip part 3

72. NexL says:

Mate are you gonna make more videos? I would really like to if you can and want. Great vid

73. Isaiah says:

all those power numbers are low by one.

74. János Gorondi says:

Man! Continue this serie! Its amazing!

75. Ashish George Aby says:

Make more

76. Thomas Philip says:

Please its been a looong time… finish what you started. Really appreciate it. 🙂

77. TomasCarrion says:

I NEED MOOOORE

78. Empty Edits says:

part 3??

79. William Mencel says:

80. shalin deval says:

81. Ludwig Ranola says:

Can you teach how source code been made from scratch?

82. INFINITE TECH says:

Great channel

83. ProjectTuring says:

Third video please !! Btw excellent stuff !!

84. isuru srimal says:

85. Rudraksh Kawde says:

When you would again start making videos.

86. Éric Duchesne says:

This video is gold, you really need to release part III!

87. Yasin Şahin says:

I didn't understand how I can make a computer

88. nathan zytkiewicz says:

when 3rd episode?!
december 2018
i want to make an computer in minecraft

89. Mohitsingh Kukreja says:

So great information so great

90. toaranthony says:

oh yes oh no…

91. Clifford Fajardo says:

WOW, this video is so well put together & it nicely summarizes the first few chapters of Code: The Hidden Language of Computers.
I came back to this video to look at a nice visual animation of counting in base 2 vs base 10

92. M says:

Maybe the reason for less number of views is that the caption and the thumbnail you used isn't that views-fetchy! If that was a reason you discontinued this series. But it's crore rupee content within! YOU ARE SYNONYM TO EXPRESSION!

93. Jason Almendra says:

Please don't be dead. I want to make a Rosetta stone of a telegraph relay computer.

94. GIrish kumAR says:

Where is 3 rd episode ……..when it will be released ……..!!!!??!!!

Where is the next video man? I need it. Don't get demotivated by likes or views. You are serving something higher than that by making us understanding computers better.

97. andykishore says:

No part 3?