Binary – How to Make a Computer: Part II

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. 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!

  2. 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!

  3. 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!

  4. 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.

  5. 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

  6. 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

  7. 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.

  8. 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! 😀

  9. 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!

  10. 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!

  11. 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.

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

  13. 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!

  14. 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.

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

  16. 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

  17. 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!

  18. 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.

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