Chuck can you count to 10 you know sometimes I wonder I try it 1 2 3 4 5 6 7 8 9 10 what's the difference between nine and 10 10 has a zero yes it has two it has two numerals in it yeah and I didn't start from zero that's fine that's fine I'm just saying one through nine all have one numeral right then you ran out of numerals yes and had to start them over over again with okay okay so go 0 1 2 3 4 5 6 7 8 9 now you start
doubling up on the numerals that you've already uttered you have a one and a zero a one and a one a one and a two a one and you already use those numerals sounds pretty efficient therein is the foundation of base 10 base 10 it's not the only way to count You Can Count other bases and it works the same way all right okay so base five would have how many numerals 1 2 3 four five and then zero so six if base 10 has 10 numerals base five has five that's what I thought I
heard you say that okay so so what are the five you don't it's got to be 0 1 two three four yes that's what it would have to five would be 0 1 2 3 4 and then when you got to five there is no symbol for it symbol for five and so five in base five would be what uh uh 40 wait okay 0 one 2 3 4 start over 1 two 3 4 0 1 2 3 4 what's next uh 0 1 2 3 4 no I'm I'm really not getting this you're overthinking
it I'm overthinking this big time I'm tell you ready I want to count in base five 0o 1 2 3 4 it's one Z 1 one 1 2 13 14 oh my God now I'm at4 I don't have any one anything left anything left so so what's my next number two two 0 21 22 4 3 0 3 0 31 32 33 4 Z No 3 4 3 4 4 and I just keep doing that you just keep doing that you with your five numbers wow you're 0 1 2 3 4 that's base five let's
go bigger than base 10 okay how about base 16 so base 16 you you use up your 10 numerals and now you need how many more six more you need six more where you going to get them from they just make letters so I will count to 16 in base 16 you ready 0 1 2 3 4 5 6 7 89 a b c d e f 16 that's base 16 okay what comes after f um give me a [Music] second 01 you go back you go back to way oh you go back to zero
go back all the way 1 2 3 4 5 six okay base 16 now wow Jesus I'm trying to I'm trying to see this a b CDE e f right and then we're at the end end of all you you used up all your numerals okay so that's so F0 you go back to the beginning so f starts the beginning zero you got to double up I'm doing the same thing again yes you are I'm doing the exact same thing again wait a minute what you gotta just double up like you've been doing with base
10 and base five I'm still missing you have 16 digits to work with right okay you used them all up okay now you got to start doubling up on them so that's what I'm going saiding wouldn't it be oh wait a minute so so then it be oh man you're getting what did you do when you got to nine I went to I I went back and it's one zero what did you do when you got to four I went back toas five uh I well when I got to four I go back back to
zero but 4 Z it was one Z I mean one zero for in base five right okay now we're in base 16 we got up to F what do you do now we used up all the digits got to go back and start over again by doubling them up that's what I said so it wouldn't it be F12 3 but no no it wouldn't f is not the beginning of the one is the beginning now double up oh one one no one zero one zero oh it's the same thing it's the same thing it's the
same thing I'm just the same you're overthinking it I'm overthinking it it's the same thing the same so it's not one zero 2 3 4 5 a b c d e f no no it is zero through F now it's okay one Zer right and now now 1 1 1 2 1 3 1 4 16 17 18 1 n uhoh one a one a oh that's one a there we go give me some fist love there next one B one c one f one F next two zero thank you two 1 2 two 2 3
three all the way up 2 a 2 B two yes F okay then 3 0 3 1 32 3 3 3 4 all the way up 3 a through F 40 41 42 4 you see how many numbers we are packing why is this so hard for me I don't know okay do you see do you see how many numbers we're packing into this because oh I can get so many more numbers out of my number line my number line now oh my gosh just increas oh my gosh number line I thought I could get
a ton the numbers out of 1 through nine or 0 1- n 0 one through F oh my gosh okay forget it forget it so now watch every computer in the world mhm has a MAC address a media Access Control address just call it the MAC address we use the decimal system that's heximal heximal heximal okay you got it that's very cool all right if you only have 10 digits from 0 to 9 right how many possible I numbers can you make that are two digits long if you have 10 digits from 0 to 9
99 99 it's 99 yeah actually it's 100 if you add the zero if you add the zero okay all right so three digits how many can you make 199 299 9.99 99 so so a thousand so so what you're doing is you're multiplying 10 by 10 by 10 all right two digits you get 100 three digits you get a th000 four digits you get 10,000 right if it's hexadecimal you're starting with 16 digits you got 16 * 16 that's 256 possible numbers in hexadecimal with two digits all right now the fun part we did base
16 base 10 base five okay how about base two all right let's let's start it off 01 boom those that's all you got to work with that's your two now you got to start over again start over again one Z one no no no no 0 one one no you start with one set of digits the next round is two sets 0 0 1 no two digits 0 one is first zero then one right what number comes next we got to start all over again yes which is zero oh one okay am I doing it
again you're all for four on this zero right one next number there's only two numbers I know so what's the next number Z One start over again start over again no we're we we exhausted the single digits correct right now you got to go to double digits so 0 one what's the lowest double digit number 0 0 no that's just zero we already have a zero okay okay 0 one right we just used up all our numbers so if you start over again and you started at 0 1 now use those numbers again but with
double digits we did this counting in base 10 when you got to n 1 one zero oh it's one one is that what comes after nine When you're counting no it's one and then zero thank you well okay so it's one zero that's correct so 0 one next number um one Z next number one Z One 01 if we were writing this down I could do it but just trying to see I'm trying to I'm trying to see it I I have to see things okay that's fine all so we have zero one we just
ran out of numbers okay now we go back like every other base you start over again with two digits one one Z right okay next we ran out of numbers again no oh one 1 Z yes what's after that 01 no a 1 0 1 0 no so it can't be 1 0 0 and it can't be one1 that's correct because there are other numbers less than that that you haven't gotten to yet you got to use up the numbers in sequence so this one zero what else one Zer one one one one one no
just one one we're counting zero one one zero one one one one okay what's next is there one two no cuz two is not in base two so what's after one one it's got to be one okay one one and then one1 there's a number less than that one z0 yes and then you go 101 thank you next one one0 give me a number bigger than that than one one0 yes it's staring at you in the face there's 101 1110 and 111 111 yeah now you just maxed out now that's one1 is like 99 or
999 now I have to add another zero so now I got to go one0 1 no just 1 1 0 next then 1 0 1 no one too many zeros okay 1 0 0 1 okay next 1 011 no No 1 0 1 0 1 0 1 0 okay one yeah 10 10 okay next 1 one no 1 Z 1 1 1 0 1 one next one one 0 0 perfect next 1 1 0 1 next 11 one zero next one 111 I think he's got this so now one Z 1 No No 1 000000
thank you next now one 0000 1 no too many Z too many zeros but you know what I mean so you know what I'm saying I play that okay here's my point I can't I can't do this without I got there's a bigger story here I got to write it down that's so weird there's a bigger story here go ahead we have 10 fingers right we have base 10 all our numbers are on this system if aliens came and they had eight fingers if they counted based on how many fingers they' have all their numbers
would not match our numbers right they'd be counting in base eight yes and you have to be able to convert if they gave us the digits of pi in base eight how are we going to know so we go to we have to be sensitive to the biases built into what it is to be human gotcha so um base 2 is the simplest of all counting systems because it only has two and uh Computing and chips and things it's binary when it say it's binary that's what's going on only two is it on or off
now in Quantum Computing it doesn't use bits it uses cubits cuits where it's not just one or zero or on or off it could be any combination of the two you can be partly one and mostly zero or partly zero and mostly one or half and half of each Quantum bits okay don't even ask me count don't you dare ask me to count Quantum bits so now here's something interesting our timekeeping is base 12 and base 60 okay okay what happens when you get to 12 you start over you start over again and the same
thing when you get to 60 okay 6 you start over again right yeah teaching Chuck how to count in base two yes without without paper it's not going to happen all right just to redeem yourself count fast in base five go uh 0 1 2 3 4 five no I'm sorry 0 1 two 3 4 1 two 3 4 okay 0 1 2 3 4 0 no 01234 you're done right next pair of numbers now 01 wait oh God all right Neil theg grass Tyson here keep looking up for
