15 and Hexadecimal - Numberphile

[@Yaymaze]

What really grinds my gears is that you write them in lower case...

[@00bean00]

Eh, that's pretty typical in programming

[@BertGrink]

Does that mean i'm doing it wrong when i consistently use upper case charaters to represent the values and mnemonics?

[@SuperSampling]

well you don't type your numbers in upper case, do you?

[@modnaryug6987]

You don't type your numbers in any case

[@dara_1989]

decimal numbers r also in lower case .... hence d matching 😒

[@TristanBomber]

"Top-end 64-bit computer". Wow, it's only been three years and I'm not even entirely sure 32-bit computers are even sold, except for niche things like the Raspberry Pi.

[@TheMrKeksLp]

+TristanBomb That is quiete strange.

[@TheVoxcraft]

+TristanBomb weird... i use 128-bit

[@TristanBomber]

TheVox 128-bit computers don't exist...

[@TheVoxcraft]

what i mean two 64bit processors in 1 pc. not the same sorry

[@DominicLondon]

+TristanBomb Even in 2012, 64-bit was very common. My PC was 64 bit at £300 when I bought it in 2009.

[@DrachenYT]

I love that just six years ago, he mentioned that "you could go out and by a top-end 64-bit computer". How quickly technology improves.

[@chriswebster24]

*buy

[@numberphile]

@looperkiller Well, I was pretty amazed he carried that TV through the physics department on his own! :)

[@Nintenrock]

6:20 That actually explains why the highest tolerance of the Magic Wand Tool in Photoshop is 255

[@EugeneYunak]

if you look closely many values that get chosen by programmers are capped at exponents of 2, or same values -1 (to account for 0), such as 2^6=64, 2^7=128, 2^8=256-1=255, 2^10=1024, 2^16=65536-1=65535 aka 65k (technically 64k), 2^32=4294967296-1=4294967295 aka 4m etc.

[@NeverInterpreter]

+Eugene Yunak 2^32 is 4 billions, not millions.

[@frankharr9466]

I'm disapointed to see that 1A is not pronounced as "Ayteen" and 1B isn't "Beeteen" and then to "Ceeteen, deeteen, eeteen" etc. I'd be looking forward to "Twenty-ay, twenty-bee, twenty-cee" etc. xAA= ayty-ay. xFF= efty-ef. :)

[@SomeRandomFellow]

i will read them like that from now on. You just enlightened me

[@frankharr9466]

I had an effect! :D I feel like Elan. Of course, I have to wonder how to seperate a0 from 80. Now I feel more like Elan.

[@SomeRandomFellow]

Frank Harr rename 8 to "oct?" Or perhaps it would be better to rename "a"

[@frankharr9466]

Call "a" "ah". So it's ah-teen, ah-ty, ahty-ah, etc. Eh, eh?

[@SomeRandomFellow]

Frank Harr lel. A3 = ah-ty-three or eh-ty-three

[@911gpd]

thank you for this clear explanation on why hexadecimal is used.

[@grande1899]

64-bit is not really top-end. Any new laptop or PC you'll find nowadays will be 64-bit.

[@SRPhantoms]

Bro?

[@huybuoi5968]

Time traveler

[@Screamintatatots]

how many bits comprise a note block?

[@ArfatXeon]

Were there any higher bit computers? No, so 64 is the top.

[@Screamintatatots]

@@ArfatXeon I mean, when someone says something is top-end, or “cutting egde,” they should be referring to a high quality product that most people do not have. If 70% of people had a 64-bit computer, it’s not really top-end, it’s the standard.

[@amihartz]

On those TI-84+ calculators, if you go to the programming thing, you can write out machine code in hexadecimal with "AsmPrgm" at the top, and then use the "AsmComp(" function and it will compile your machine code to a program you can run using the "Asm( function.

[@Acid113377]

as soon as I saw the guy known to me as "the amazing pacman dude", you got a like & fav. from me... I truely enjoy your videos Brady, thank you very much for entertaining me time and time again!

[@U014B]

4:52 That's not an f, that's a ք.

[@fakedeltatime]

+Noel Goetowski I believe you mean Ք. Or at least I think it looks more like it. The other ones are lower case, so I don't know.

[@U014B]

+Neko Haxor That's exactly the letter used, but I guess it was a different font.

[@gFamWeb]

+Noel Goetowski It's simply a f with the top curve arching back down. sort of like a cursive f.

[@U014B]

+Noah Gregory Just repeat to yourself, "It's just a joke; I should really just relax."

[@emajekral]

A two digit hex number has a 16's place and a 1's place, similar to the decimal 10's place and 1's place. To do the conversion between hexadecimal (hex and decimal, multiply the digits by the value of their place. eg: decimal 99 is 9 * 10 + 9 * 1 = 90 + 9 = 99 hex ff is 15 * 16 + 15 * 1 = 240 + 15 = 255. Each of the hex places is a power of 16, just as each decimal place is a power of 10.

[@Aquallie]

I love this stuff. I work with a major project in school this year, which I have to pass or otherwise I won't get my exam. I choose to do this project about bases, and numberphile videos help me much with this. (The base 12-video actually inspired me to do it.) I'll be glad to write numberphile as a source of my work when it's done!

[@ThomasEdits]

did bro get his exam

[@CaseyShontz]

There are 16 types of people in the world Those who understand hexadecimal And F the rest

[@00bean00]

*10

[@nathanliu2031]

wow I came up with the same joke as you! I guess great minds think alike

[@FineLime]

Um, you still have to list 20 more types of people

[@TruthNerds]

Only one in 10 people understands hexadecimal. That's 6.4 percent.

[@randomguy263]

@@TruthNerds Why would they use percent? Percent is base 10.

[@EGMusic12]

“top end 64-bit computer” - 2020

[@samstewart4444]

I feel so very old watching this video. My career was programming in c using vi as the text editor.

[@harry_page]

I remember in school I used to have an old model of scientific calculator, and it had a hexadecimal mode on it. I noticed that letters started mixing up with the numbers so I put 1+1 then kept pressing equals to count up and saw that way of counting. Confused me a lot but it had me interested!

[@TruthNerds]

Nitpicking: 255 is not the highest value an 8-bit computer can store. It's just the highest value an 8-bit computer can store *in a single memory location or register* . You can do multiprecision arithmetic (which is completely analogous to pen and paper long addition, subtraction, multiplication etc.) on numbers larger than what the CPU supports directly. That's how you could keep track of 5 digit or longer score counters on 8-bit computers, for example. As a side note, there is even a much faster algorithm for multiprecision multiplication than long multiplication for huge numbers that is used on many computer systems nowadays. It's based on the Fast Fourier Transform (FFT) algorithm and called Schönhage-Strassen multiplication.

[@mkaatr]

Wow... this brings back memories. In the computer science class we had to compute in binary, hex, and also in octal (which uses 8 numbers from 0 to 7).

[@ajuk1]

Gota love big old Teles before the days of Flat screen and HD they could still keep up to date even if they were 20 years old, I used to have one and I had a Freeview for the signal and I had that plugged into my Stereo for sound.

[@86Ivar]

64 bit computers were considered top notch in 2004-2005.

[@aMpeDDUp]

@JizzleonmyTiggles this has to be one of the best comments I have ever seen in all of my days. well done sir, well done.

[@j0h00]

What annoys me is trying to expain different bases (base 2, base 12, base 16, etc) to other people... This stuff SHOULD seriously be taught in school!

[@cgaccount3669]

I learned it in high school. both in math and electronics courses. In Canada. That was in 1981 when our entire school had 2 whole computers. Strange if people aren't shown this now in school

[@HadiAhmed098]

+CGcomment Account I can say with relative certainty that ~70%of my school has no idea about this stuff. I live in America and have taken up to A2T&S

[@cgaccount3669]

J0h00... I was also taught different bases in high school math class in Alberta Canada. But who knows if they still teach it. Seems like all they do from what I hear is watch movies and have all kinds of holidays.

[@thegoodkidboy7726]

Base 5 (Roman numerals) are taught. At least in my primary school.

[@neoxus30]

I wouldn't consider Roman numerals as quinary system, i think they can't be considered a base)

[@somewony]

"Or you can go out and buy a top end 64 bit computer" And at this point i realised how old this video is.

[@secularmonk5176]

I was anticipating this vid to be about how the properties of 15 in hex mirror those of 9 in dec. I'm rather underwhelmed. Even as an introduction to "why hexadecimal?", this is pretty clunky. Although I did like the ancient tech intro.

[@joealias2594]

The reason why is because computers use binary and hex makes it easier to relate numbers to binary. That was the point of the video.

[@radiowwww]

Thanx for the hexadecimal lesson. You made it so easy, i started a playlist with your video first, and then subscribed to you channel. Thanx again.

[@raptorphobic]

I count in base 21

[@kellel5610]

Stephen Smith i count in base ten

[@jonathanschossig1276]

Base 65536 is way better.

[@om-ni]

why base 21?,?

[@EGMusic12]

I count in base 12

[@V1C.T0R]

I count in base 2.

[@ryanprov]

Missed opportunity to talk about the best bit of naming in this topic: each hexadecimal value represents four bits, or half a byte of data, which is called a nibble -- two nibbles makes a byte!

[@tracyscanlon4587]

What's the tv for?

[@unounk9415]

It's the monitor to show that the computer counts in base 16

[@00bean00]

To lift weights

[@ChikoWhat]

That explains 'a lot' for me about hexadecimals AND counting in bits. Helps me when I'm tinkering with games. Awesome.

[@pacoo3712]

I've heard of government computers passing 64bits, its that true?

[@Nero_Freeman]

No. There is absolutely no reason to have 128 bit (The next step up) machine, at least for the next several decades. The current limit with 64 bit is theoretically 18,100 TB of ram. You might remember the 3.2 GB ram cap of 32 bit. There is no single machine in existence that even has that much ram, the closest being the Tianhe-2 supercomputer with 1,024 TB of ram. Supercomputers although are not applicable since they are multiple machines joined together.

[@Nero_Freeman]

Yes, but both of those are also irrelevant since they have made progress to make that a non-issue on 64-bit systems. They can make data that theoretically should not be possible in a 64 bit system work, but they cant do that with ram currently.

[@JusticeRetroHunter]

one of the most informative videos ive seen so far. i had no idea how binary worked until this vid!

[@Badplum25]

What can I gain by learning how to read binary and hexadecimal numbers?

[@juggernaut1011]

Knowledge? fun? . . understanding of multiple number systems? . . . . . fun? idk

[@stevefrandsen7897]

Comes in handy (or necessary ) in a computer type of career. You never know the numbering schemes you may run into. Plus the next numbering scheme that you HAVE to learn will just be "the same thing only different".

[@binley2]

The register your central processing unit used to store this sentence at the moment it was being decoded contained binary digits. If I looked at the contents of your register at the very moment it decoded the previous sentence, it would output the hex version of the contents stored in it. Because reading 2A3432903932B3B4 is much easier than reading 01010100 01101000 01100101 00100000 01110010 01100101 01100111 01101001 01110011 01110100 01100101 01110010 00100000 01111001 01101111 01110101 01110010 00100000 01100011 01100101 01101110 01110100 01110010 01100001 01101100 00100000 01110000 01110010 01101111 01100011 01100101 01110011 01110011 01101001 01101110 01100111 00100000 01110101 01101110 01101001 01110100 00100000 01110101 01110011 01100101 01100100 00100000 01110100 01101111 00100000 01110011 01110100 01101111 01110010 01100101 00100000 01110100 01101000 01101001 01110011 00100000 01110011 01100101 01101110 01110100 01100101 01101110 01100011 01100101 00100000 01100001 01110100 00100000 01110100 01101000 01100101 00100000 01101101 01101111 01101101 01100101 01101110 01110100 00100000 01101001 01110100 00100000 01110111 01100001 01110011 00100000 01100010 01100101 01101001 01101110 01100111 00100000 01100100 01100101 01100011 01101111 01100100 01100101 01100100 00100000 01100011 01101111 01101110 01110100 01100001 01101001 01101110 01100101 01100100 00100000 01100010 01101001 01101110 01100001 01110010 01111001 00100000 01100100 01101001 01100111 01101001 01110100 01110011 00101110

[@2Cerealbox]

Badplum25 You'll understand how your own base system works by understanding place-value-notation better. Also, while hexadecimal isn't super useful even in programming, at least colors are still represented as three, two-digit hexadecimals numbers for Red, Green, and Blue levels. If you want to create a custom theme of your computer or in a power point presentation or something, it's useful to know that when you see something like "#000AFF" that's referring to a color that has no red in it, that's a dash of green in it and the maximum number of blue in it - in other words, it's a sort of pleasant, slightly subdued, blue shade. Also, you're going to need to know hexadecimal after the robot uprising.

[@JustPingo]

Badplum25 Also button management il many video game console is used with binaries operations. For example pressing only A would output 001, pressing only B 010 and pressing both would output 011. So by knowing how it works you can deal with it when you program games on video game consoles. I hope I was clear lol

[@RufusShinraPower]

Whenever I played (and still do play) my Sonic 2 game for the Sega Genesis, in the options menu would be the sound test and the number went like 1,2,3....1A, 2B, 3C or something like that. I was curious about why that was and I am glad that I was able to find out in this video.

[@007MrYang]

Everything becomes f

[@noncanadian]

whenever i get up in the morning, i always wonder... am i really the same person i was yesterday?

[@killeramaru]

Just to give you an update, I've watched a lot of the videos on this channel ever since I subbed them, and they are "sub worthy". After subscribing to this channel I soon learned of other similar channels and I thank this channel for it. I've learned a lot of new things as well as cleared up some misconceptions (thanks to 1veritasium). All thanks to this video.

[@kent631420]

the highest number in 32 bit is 4,294,967,295 16 bit is 65,535 8 bit is 256 4 bit (also known as 1 byte) is 16

[@SomeRandomFellow]

isnt a byte 8-bit?

[@plasticlobster23]

Yes. 8 bits per byte. 4 bytes is a nibble. That is, by modern standards. Technically speaking hardware manufacturers can define their byte size to be anything they want simply because a byte is the smallest addressable area in memory.

[@SomeRandomFellow]

Joshua Mullin did not know that. interesting

[@plasticlobster23]

Meant to say "4 bits is a nibble." Was a typo.

[@SomeRandomFellow]

Joshua Mullin lol i misread your comment as "4 bits is a nibble," read your next comment, then got confused

[@oliverbeagley]

It's because F is the 16th number not the 15th (you have to start counting from 0). So you square 16 which equals 256. So when two hexadecimal digits are put together to be one number (as in FF) the maximum number of numbers possible to be created is 256. Now you have to remember that 0 is also a number considered for this so you drop 256 to 255 to show the highest value for two digits.

[@leo2895]

Why at 6:19 xFF is equals to 255? It confuses me because he said that F = 15.

[@Ace8080]

F alone equals 15 (1111 in binary). FF is 11111111 in binary which is 255.

[@leo2895]

Oh I see, thanks.

[@SimplyMyAccount]

leo2895 I like to think of it like hexadecimal has 16 possible values (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F) and if you have 2 digits then thats 16 possible for the first one and 16 possible for the second so the largest number is 16*16=256 but you have to subtract 1 for 0. You can also do it like 15*16^1+15*16^0 = 255. Which is useful for large numbers cause you can do a 4 bit hex number (lets say 9A3D) = 9*16^3+10*16^2+3*16^1+13*16^0 = 39485.

[@kimf.wendel9113]

leo2895 Yea he relly didn't cover that. but when you count, you just add a digit in front when you run out of numbers and the start over, for instance 10, is 1 and 0 because you start over. The you reach 20 and you've counted 10 numbers two times. At 99, you have counted to 10 9 times, and then 9 more. Going hexadecimal is the same thing, when you hit 10 you have counted 16 digits thou, so at FF you have counted to 10 (16) F (15) times and then another F (15) - so 16*15+15 = 255.

[@kimf.wendel9113]

***** do note, that is binary, not hexadecimal. Although they are the same there are it's a longer process to arrive at the result if you used a different number to convert

[@ohwhererehwho]

Enlightening... numbers make so much sense that it's a true-false comfort to know they are there, even if oddly reduced into complex-simple zeroes and ones and

[@Ian-pc5it]

There are 10 kinds of people in this world...those who understand binary and those who don't.

[@ErizotDread]

this brings back memories of my commodore 64 and using my DI-Sector program to alter games using hexadecimal...I think one of the major telltale signs of geekdom is how much time you spend in your bedroom doing things other people would find mind numbingly boring and loving every hour of it! lol

[@naimulhaq9626]

Mr. James Clewett is it true that we find counting in base 10 easy because we have 10 fingers? I think there must be some mathematical reason. For example primes in base 7 can be even, the prime 11 in base10 is 14 in base 7 and similarly other bases has properties like the one above, except base 10 which seems to be unique, and the properties of base 10 are not shared by other bases. Why?

[@Ruminations09]

Actually, you're just thinking of systems that have an odd number base. For literally every even numbered base, this isn't true. In fact, it isn't even true of systems that have an odd numbered base, because the definition of an even number is that it is divisible by 2, and 11 isn't divisible by 2 regardless of if it's written as 11 or as 14. And yes, pretty much the only reason we use a base 10 system is that we have 10 fingers. A better system that would have been nicer to adopt would be a base 12 system. Base 10 is a bit sloppy, because the only numbers divisable by 10 are 1, 2, and 5. However, 12 is divisable by 1, 2, 3, 4, and 6 - 2 more digits. - The reason why this is helpfull is that a lot commonly used frations become a lot more practical. The most used fractions are probably 1/2, 1/3, 2/3, 1/4 and 3/4. With base 12, 1/2 changes from 0.5 to 0.6 - not a change of any singinifcance. But 1/3 changes from 0.33333333333333(into infinity) to 0.4, a lot more manageable, and 2/3 similarly changes from 0.66666666666(into infinity) to 0.8, again, much more manageable. 1/4 changes from 0.25 to 0.3, and 3/4 changes from 0.75 to 0.9, so this isn't too much of a change, but you eliminate one digit, so it's still an improvement. Sorry, I went off on a tangent there, didn't mean to. Basically, there is no real reason that we use base 10 except for the fact that it is the number of fingers that we have.

[@naimulhaq9626]

PokemonTom09 I am glad you went a little tangent, I am sure you will not mind if I do the same. In number theory, properties like divisibility, odd/ even, primes, sloppyness, logarithmic representability, and many others are not the same for the different bases and seems to have a sense of intrinsically referring(like a datum) to a sense of uniqueness of base 10. Am I surprised for no reason?

[@Ruminations09]

Naimul Haq I suppose that is a fair point, and intresting observation. While I definately think things like this are worthy to note, I still think it's mostly down to coinsidence (which I suppose is just more reason to be surprised)

[@naimulhaq9626]

Daniel Cannata Thank you. I know of Brady's video. I was interested in knowing if there is an academic discourse on the uniqueness of base 10.

[@joealias2594]

Naimul Haq Name an actual property of base 10 that another cannot have.

[@Styleth]

@numberphile James Clewett is like the biggest/strongest scientist i have ever seen! O.O DAMN!

[@jomiga1999]

Efty Ef

[@colitipal]

The highest value that a 64-bit computer can handle is 18,446,744,073,709,551,615 from 0.

[@deschmichael]

0100 0000 0000th comment.

[@s_hietsch]

+Mike Desch Liar, Im only 0011 1100 1000th comment

[@Savageboi506]

I'm 1011th

[@Kyuubi840]

It can always store two groups of 4 bits each, and remember to read them in sequence when it needs to print the 'a'. There's the problem of Endianess (which 4-bit-set should come first?) but that's just a matter of deciding on one way and use it consistently.

[@deannarobles2700]

How about that?

[@RealCadde]

I am 29 now and i learned about this 16 years ago. It's not strange at all for you to know it, it's rather common knowledge now with computer users. It was different in the past, if you tried to teach others how it worked that wasn't interested in computers they would call you a computer geek or nerd. Today's kids don't seem as keen to make that distinction any more.

[@k.chriscaldwell4141]

Remember, computers, unless something exotic, only utilize binary. Hex, Octal, etc. are only for the benefit of the human developer and/or user.

[@MikeWalkerPhd]

Interestingly enough the Acorn Electron's OS actually technically isn't even a full DOS (support for disk drives was an optional extra however) - it was called Acorn MOS and it used cassette tapes only (where data is read off in a 'stream'), it had no support (without buying seperate extra hardware) for what are called 'block-level devices' where data is access in chunks (like disk drives). Just thought you'd be interested to know...

[@1959Edsel]

You can count in hex on your hands. Each finger has three joints. Using those and the four fingertips, you have 16 places that the thumb on the same hand can point to. Do the same on both hands and you can count to FF (255).

[@k.chriscaldwell4141]

_Code-The Hidden Language of Computer Hardware and Software_ by Petzold is an incredible book. It shows how the bits and bytes in a computer are formed in to commands the computer understands. A wonderful book.

[@MPSpecial]

Press 15 to pay respects

[@HGHStudios]

Shoutout to the little bit of spit/food that shoots onto the table at 5:29.

[@AtactHD]

@JohnDCrafton i think he builds alot of circuits and stuff because on a seven segment display you HAVE to use "a, b, C/c, d, E/e, F"

[@RealCadde]

Further details! There is one other commonly used numeral system on the PC and that is the 'Octal' (8 variations) that is used in Unix based systems as an example. Octal can represent 3 bits and are most commonly used as a "on/off" switch for file permissions. Read, Write and Execute respectively! There are 3 permission "categories" per file, Owner, Group and Others respectively. So to set full permissions to all you would set it to Octal 777 (representing 111 111 111 or all 'on' for R, W, E)

[@dipsht131]

hex: 1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,10 where 10 is actually 16 in hex. if you convert to binary and assign each digit in hex to a set of four bits, this counting makes sense: 0001 0000 is 16 in binary and hex allows one to simplify that whole chunk into one symbol. ex. 1111 1111 would be FF in hex

[@Weiss.Schnee]

Could you consider doing an episode on imaginary numbers such as Ln(-1) being i*pi and Rt(-1) being i and/or irrational numbers such as the exponential constant and pi itself? But obviously, making the episode about DIFFERENT irrationals and imaginary numbers, such as the golden ratio :D

[@AlbertTheGamer-gk7sn]

Also, if ln(-1) = i*pi, the integral of 1 to -1 of the function 1/x respect to x is i*pi, and the integral from -1 to 1 of the function 1/x, which produces an indeterminate infinity-infinity form, will be -i*pi.

[@ananiasacts]

I started out programming the Monrobot XI (a minicomputer from Litton Industries which had a 2000 16 bit word memory on a drum--no RAM which was "cores" in those days) and they use the letters S through X instead of A through F to represent the hex numbers above 9.

[@BGBTech]

well, there are these: base 36: 0-9, A-Z base 64: A-Z, a-z, 0-9, +, / base 85: errm... these can be a little more compact than hex, but aren't nearly as human-readable. hex: 32-bits in 8 characters; base-64: 32-bits in 6 characters; base-85: 32-bits in 5 characters.

[@Gmackematix]

If you are watching the Numberphile episodes in order this video says that in hexadecimal we use bumfit digits or digits that go up to the first non-trivial Marsenne non-prime.

[@Tony72495]

Actually never mind, I understand now. See originally when the console wars really started, 8-bit did refer to the processor, and so did 16-bit and 32-bit, but when the 64-bit and so on generations started, they seem to have switched over to using the memory bus size to make the number seen larger, so like the PS3 could be considered a 128-bit console, but that's the memory bus size. At least that's what seems to have happened.

[@JasonKatsanis]

Well, it works like this, Hokage: every time you press key or click a mouse button, it sends a signal to a little man inside with a pencil and a pad of paper. He writes your command down and slides it down a wire, where it hits squirrel on a wheel, who then tries to run away. This is what causes the whirring sound you sometimes hear. Then, just like the distributor on your car, it sends each pixel to your screen. And that's how a computer works! Fascinating, isn't it?

[@KeenanTims]

@hedbiter Partly convention (computers have worked with 8-bit bytes for a long time) and partly because 16 combinations/symbols is easy enough to memorize and get comfortable with mentally. 3-bit groupings (Octal - using the symbols 0-7) is also somewhat common and many programming languages support this as well.

[@flowertrue]

I love this kind of stuff. Back in the 80s I programmed my Commodore 64 (pause for laughter to subside). I do wish I'd kept up with programming, I'd probably be rich now. I don't recognize your first computer there, and I knew quite a few in that generation. Maybe its a brit thing. It was my understanding that you used the # to indicate hexidecimal numbers as in #003366

[@marksusskind1260]

I was a child in the 1970s, and there was a series of short episodes called Schoolhouse Rock. When they would cover Multiplication Rock, one of the cartoons lectured about multiplication by 12, presented as science-fiction with an extraterrestrial visitor. They introduced digits DEK, which resembled lower-case chi [Greek], and EL, which resembled lower-case epsilon [Greek], to represent 10 and 11 units respectively. I thought that they were real digits, so I brought them to class several years later, much to the amusement of my classmates.

[@evenprime]

Base 16 uses 4 bits. That's very comfortable to work with, because 1 byte has 8 bits and therefore can be represented by 2 symbols (0-9 or a-f) in hexadecimal. A 16-bit number can be exactly represented by 4 symbols, a 32-bit number by 8 symbols etc. With base 32 you'd lose that simplicity, because base 32 uses 5 bits and 8, 16, 32, 64, 128, ... can't be divided by 5. Also, it is a lot easier to memorize the decimal (and binary) value of only 6 letters instead of 22 letters.

[@AntonijnB]

You're correct, but I didn't want to go into that detail. The reason that -1 is 11111111 in binary btw, is because of the way computers subtract numbers. For an ALU, x+y equals x plus the inverse of y plus one. -1 is essentially zero minus one, so let's see what that gives us: 00000000 + invert(00000001) + 1 = 00000000 + 11111110 + 1 = 11111111

[@AlbertTheGamer-gk7sn]

Also, negative binary numbers have a 1 on the leading digit of the leading nibble, and have a leading hexadecimal digit of 8, 9, or the letters.

[@ChikoWhat]

@anubisxdmj0 instead of going 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to 10 (20, 30 after reaching 9 each time))then adds 1 to the next unit it goes: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f THEN it adds 1 to the next unit which becomes 10. from 10, add 9 then the 6 letters again before going to 20. Instead of taking 10 jumps to reach the next unit (The 'tens' unit) it needs to jump 16 times to 10.

[@airman122469]

I was saying that your statement of CPU's getting phased out of "extreme use" was wrong. Also, the reason that Minecraft, a game with a lot of visual output, is faster on a computer with a GPU, is because graphics (the G in GPU) get directly processed by the GPU. There is still a lot of program control flow that has to be handled by the processor.

[@KilloZapit]

Actually, it's not about a cpu bit value, but it's byte size. Nowadays more or less every cpu uses 8-bit bytes, even 32 or 64 bit ones, but byte size is actually system dependent. That's why in technical specs for network protocols and such you see the word "octet" instead of byte to mean 8 bits. I am pretty sure Octal was mostly used on computers with 6-bit bytes, of which there used to be a few. Hexadecimal was always more geared to 8-bit bytes so it has more or less replaced octal.

[@Keelyn1984]

Don't forget that many home computers only had a 7-bit architecture.back in the day until the release of the Personal Computer made 8-Bit really popular. Even the original ASCII-Code was based on 7-bits.

[@MattMcIrvin]

The Honeywell mainframes my dad used in the 1970s often used octal (base 8) instead, in which the digits only went from 0 to 7, and every digit represented three bits. That was convenient because those machines actually had a 36-bit word, a multiple of 3. These days, usually every processor uses some power of 2 of bits and hexadecimal makes more sense. But I think the C programming language, and its predecessor B, were originally developed on DEC and Honeywell machines that had 18- and 36-bit words. So octal was preferred. And that's why numerical constants in C, and all of its descendants like C++, Java, Javascript, Perl, etc., are slightly easier to write in octal than in hexadecimal: beginning a constant with the digit 0 identifies it as octal, whereas hexadecimal constants begin with 0x.

[@JBroMCMXCI]

'1' has value one no matter what base you're in

[@thegoodkidboy7726]

base 1/2

[@neoxus30]

base 1/2 would be 2^-n)

[@AbominableSknowman]

This video was made over a year ago. That means that 64 bit computers were "standard" for only two years. He did say recently, which meant two years, in this case, which is fairly recent. I'm currently using a 32 bit computer, and many people that I know haven't upgraded yet either. Just because 64 bit has been more common since 2010 doesn't mean it's standard.

[@noblessus]

The method you just described is known as Horner's Method. Pretty cool stuff.

[@raxa45]

love this vid, such an insight and now i see why collours are coded as they are

[@DelusionalLogic]

Natively the cpu still only operates with 8 bits, you just have two variables, and then you convert that into 16 bits in low level software. You have to remember the difference, A 32-bit version of windows can operate with Qwords too, you just need to bit-shift/compare the values into 2 32 bit dwords. (Commonly the bit's refer to the internal wording, not the variable length)

[@47f0]

Unless, of course, the computer you're using is an old Univac - they used a triad of 3-bit nibbles to make up a 9-bit byte and four 9-bit bytes made a 36-bit word, so Univac programmers got comfortable reading dumps and machine code in triads of octal (base 8), rather than hexadecimal (base 16).

[@duocentillion]

It's an arbitrary choice to represent a single digit in a 16 digit counting system. We used the letters A - F because they were available.

[@Metallosaurus]

He was pointing out that 3 years isn't "new" in technological progress time. Sometimes it's better to forget about the big picture.

[@MrRenseck]

That man makes the best accolades I've ever seen.

[@BGBTech]

there is also the 128-bit oword (octoword), though some people call it a dqword (double-quad-word), allowing for a 256-bit qqword (quad-quad word).

[@RealCadde]

Hey, i don't have a masters degree in computer science and i knew everything about this already. It never fails to interest me to hear how people choose to describe it.

[@JonSneyers]

This video should also have talked about how colors are represented in HTML (or CSS): e.g. #FF00FF is purple because these 24 bits indicate the brightness of the RGB channels, and 100% red, 0% green, 100% blue will give you purple. If you would show that number in decimal, it would make no sense at all, but in hexadecimal you can imagine what the color looks like just by looking at the number.

[@cbernier3]

@Redtim911 yes, that is how binary works, the same way as decimal and hexadecimal. F00 = 256, F0=16, B=11, so FB=27

[@chrisg3030]

Another point of comparison between base sixteen and base ten is that 16-1 has two distinct prime factors, 5 and 3 while 10-1 only has one, that is 3. This has relevance for the symmetries of 37 (base ten) discussed in another Numberphile video. We know that any three repdigit in decimal, such as 444, is equal to the sum of its digits multiplied by 37. The number that does that trick in hexadecimal is 5B (equal to 91 in decimal). But there's also a number in hexadecimal which will do the same for a five repdigit. For example 44444 divided by the sum of its digits will give 369D, as will 11111, 22222, FFFFF etc.

[@radnyx_games]

Octal is also represented with just a 0. So octal 777 would be represented as 0777.

[@RealCadde]

Storage has nothing to do with it, data is stored in bits. (0 or 1 value) The reason they use hexadecimal is simply because the first data stores used 4 bits (called a "nibble") and so, the highest number of variations you could have was 16. Hence they use hexadecimal representation. Octadecimal represents 18 numbers (up to letter 'H') so that would mean you would need a computer that works in ternary to make any sense and 3 'trits' to represent that number.

[@AlexanderKrivacsSchrder]

It's because your calculator is using signed 64-bit numbers, stored using two's complement. I don't know if a video was ever done on that, but if you look up "Two's complement" on Wikipedia, you'll soon know the answer.

[@thecoshman]

you seem to have misunderstood. In the normal numbers system we use, decimal, you have ten (hence decimal) digits, 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. In hexadecimal, you have an extra six digits, A, B, C, D, E and F. In binary you only have two digits, 0 and 1. So you see, you can not have an 'a' in binary, but you can represent the hexadecimal value A in binary as 1010, or in decimal as '10'. That is three representations for the same value. Does that make sense to you?

[@Shadow10Hunter]

This is possibly that most interesting thing I've seen all week O.O

[@SirReptitious]

@Surfurplex It's because computers start counting from zero, no matter which base number system they are using, where as we start from one. So they actually DO use "square" numbers, just not the ones you are used to. ;-)

[@gesh92]

Back in 2000 my family couldn't afford a modern computer so I used one with similar capabilities. And that is how I began programming at 8! I didn't really have many games to choose from :D

[@RealCadde]

Like i said, there are several 32 bit systems out there still and you have to remember the Steam survey is targeted at gamers who tend to upgrade their systems. The majority of the worlds computers still have 32 bit processors. And it doesn't matter if a 64 bit processor costs more or less than a 32 bit one as far as upgrading goes. It still requires a whole new computer. May be why he said higher end, because once you upgrade from a 32 bit you have no choice but to get a powerful one.

[@AlexanderKrivacsSchrder]

Except they don't mean numerical bases like hexadecimal in that case, it's an encoding system used to be able to represent any byte value (0-255) inside a more narrow range of byte values, such as the alphanumeric characters. This is used to you can transfer binary data in a system where binary data typically would get mangled because the system was coded to only accept printable characters.

[@roberthoople]

Coming here from 2020 to reminisce about 64bit computers being the new thing.

[@looney1023]

@uut0 those numbers aren't really about each. 2^10 is 24 more than 10^3. thant's not too bad, but 2^20 is a whole 48,576 higher than 10^6. And 2^30 is a whopping 73,741,824 higher than 10^9