Base 1010 and the Realm of Number Representations

Outside our typical way of viewing numbers, there's a whole realm of different representations each number has. Follow me into this realm to see a bunch of awesome patterns that not enough people know about!

Do you have any old clocks or other items you'd like to see in the background of my future videos? Well, like I mentioned at the end of this episode, I have a new private mailbox where you can send things! If you might want to send anything, watch this short video on my ‪@Domotro‬ channel which contains some brief guidelines and the mailbox address:    • Видео  

By the way, to clarify: in this episode, I’m using the word “numbers” to mean base-independent amounts of things (and only positive integer amounts, along with sometimes zero), and I'm using the word “representations” to mean the strings of digits that can express numbers in different bases. For the type of bases that I was discussing (positional numeral systems based on powers of an integer larger than 1), I nicknamed them "basic bases", which is a term I might continue using in the future, since there are many patterns you can say are true for "all basic bases", but which might not hold for "all bases" in general if you include things like tally marks or some of the more obscure bases I've covered in past episodes.

I didn't put any background music in this episode like I usually do, because there were a bunch of birds making nice sounds in the background the day I filmed this, and I wanted to let you appreciate the Combo Classroom's natural soundscape for a bit!

If you enjoy this episode, make sure you've checked out these other episodes on my channel about some rarer types of number bases:
How to Count in Base Negative 10 -    • How to Count in Base Negative 10  
How to Count in Fractional and Irrational Bases -    • How to Count in Fractional and Irrational ...  
How to Count in Base 2i -    • How to Count in Base 2i  
Also here's my episode about "highly composite numbers" -    • Why the Number 1,000,000 Should Be 1,081,080  
And here's one of my episodes about "modular arithmetic" -    • Modular Multiplication Magic  

Check out my Patreon at   / comboclass   if you want to support the channel, get some cool bonus content, and get your name on a whiteboard in the Grade -1 finale! Thanks to all of my supporters there:
George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Max, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Amy, Izeck, and Beugul.

If you use Discord, join us on the Combo Class channel where there are lots of fun conversations going on:   / discord  
There's also a subreddit at   / comboclass  
And make sure you're also subscribed to my other channel ‪@Domotro‬ for my shorts, livestreams, and bonus videos.

[Some topics mentioned in this episode include: positional numeral bases, bases that consider themselves to be called “Base 10”, the last digit of numbers in different bases, what it means to end in a 0, prime numbers, highly composite numbers, square numbers, cube numbers, perfect powers, factors/divisors, modular arithmetic, and more!]

DISCLAIMER: never try to copy any physical actions you see in Combo Class, such as anything involving fire, tools, science experiments, or falling clocks.