The Base Some Computers Use Instead of Binary

Most computers use binary, but some actually use a lesser-known base called "balanced ternary". Let me show you how that cool base works, starting with some puzzles and building up to some awesome mathematical abilities that "balanced" bases have! (see below for links to the other videos I've made about different bases)

To clarify a few things people asked about in the comments:
-- Some people in the comments seem offended about the laptop destruction. That was not a functional computer. I would have needed to dispose of it in any case. I just had fun using it as a prop first.
-- Yes, ternary computers have actually been made before! For example, some were manufactured by the Soviet Union in the past. They have never been as widespread as binary computers, but you never know what the future may hold!
-- In the weighing puzzle, by "test" the weight of a target item, I mean that you have to find a way to "equal" the item's exact weight (as if figuring out that it is a particular weight and confirming it is precisely that)

Here are some previous episodes I've made about different bases:

By the way, I've started putting shorts on this channel but they typically won't go to notifications or subscription feeds (they typically have been on my @Domotro channel and did so well for that channel that I want more people on that shorts page to find this channel too). They will be available on the "shorts" tab on this channel, and I will link the recent ones in video descriptions like this. Here are the two I've put on this channel so far:

Special thanks to Evan Clark and to all of my Patreon supporters:
Max, 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, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, and Julian Zassenhaus.

Domotro
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Berkeley, CA 94709

If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)com

In case people search any of these words, some topics mentioned in this video are: balanced base 3 (balanced ternary), weighing puzzles that encode numeral bases, other balanced bases, symmetry, truncating numbers vs. rounding numbers, a possibility for a ternary currency system, the powers of 3, threevens vs. throdds, the mathematician donald knuth, how and why most computers use binary compared to some computers that use balanced ternary, and more!

If you're reading this, you must be interested in Combo Class. Make sure to leave a comment on this video so the algorithm shows it to more people :)

DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.

[ComboClass]

Thanks for watching! Check the description for links to the other episodes I've made about different bases.. Also to note: a lot of people seem offended about the laptop destruction. The computer I used as a prop was completely non-functional. I would have had to dispose of it in any case, I just had fun using it as a prop first.

[Cattingslan]

The way you made the 1 and -1 look like up and down arrows made me think of the spin of elementary particles

[asheep]

0:00
Laptop damaged 0 times!
0:21
Laptop damaged 1 time!
7:09
Laptop damaged 1T times!
15:43
Laptop damaged 10 times!
16:44
Laptop damaged 11 times!
16:55
Laptop damaged 1TT times!
This list is a dynamic list. You can help by expanding it.

[thalt]

Combo Class: 50% education, 50% things falling and breaking

[KarolOfGutovo]

Balanced bases do be wacky. I sure do wonder if balanced ternary could have been more popular if binary didn't emplace itself so strongly.

[lexinwonderland]

this channel is a perfect mix of Tom & Jerry level slapstick and fantastic educational content

[DeWillpower]

that's very cool to know, while watching i was imagining myself discovering an alien society using this method because i watched some of those videos that are like "what if the aliens use a different system of [doing a specific thing, like math] to ours?" and i finally found one and it's gorgeous

[ladislavseps]

This i my favorite number base.. Just the number of "not so boolean" operations you can do on balanced ternary digis..

[RecreationallyCynical]

The biggest reason why binary is used in computers as opposed to ternary (balanced or unbalanced) or even biquinary is because of it's electrical simplicity. You have two voltages your gates need to maintain: +5V and 0V. If there were any voltages greater than 5V they would be treated as 5V and therefore ON, and any voltages less than 0V would be treated as 0V and therefore OFF. When you add other voltages in the middle, things get tricky because you would need to ensure circuits at the middle voltages don't "drift" into one of the outer voltages. Any amount of inductive or capacitative interference, or a power flicker, could cause some node at a middle voltage to waver toward one of the outer voltages, which can corrupt the data if later circuits incorrectly read the value.

Also, Donald Knuth's last name is two syllables: kuh-nuth. You pronounce the K separately

[josephrissler]

I think the reason we keep using binary isn’t because of the physical manufacturing logistics, but the fact that all out algorithms are built with binary in mind. A binary circuit can still use ternary by using 2 bits per… Trit? Trigit? The fourth symbol could be used for special purposes in some contexts, or even be the same as 0 to allow for “lazy normalization”.

But even without the history of base 2 in computing, most “divide and conquer” algorithms work naturally with base 2, since you want to divide your problem into the least number of chunks (i.e. 2) for efficiency reasons.

[areadenial]

OH MY GOD YES! I love balanced ternary so much, I've been waiting for this video for a long time!

[nitehawk]

Donald Knuth's latest book just came out Book The Art of Computer Programming 4B. Its basically a series of computer based math problems.

[frechjo]

I love balanced ternary.

You know how they say that there are +- types of people...

[jelenahegser]

you can also do balanced bases for all natural numbers greater then 2, not only the odd ones. For an n-digit balanced numbersystem, just take 0 and the (n-1)st roots of unity (in the complex plain) for n=4 (or n=7) it is very beatuful, as it lets you calculate in the Eisenstein-Integers very easaly.

[hgilbert]

i can't believe i watched the whole video.
super tired, and thought: ok, just a preview.
but so interesting, kept me in suspense: how would that work, then? ...
and very well explained in the end.

[NickWrightDataYT]

"But what about the True/False-iness of Binary? What's the third option gonna be, 'I don't know?' LOL"

Yes.

[danielrhouck]

In the case where your testing weights can only go on one side, you donʼt actually need a 1 weight. Suppose you want to measure something that weighs 35 units. Then you can use the 32 and the 2 to see it weighs *more* than 34, and the 32 and the 4 to see it weighs *less* than 36, and youʼre assuming it has an integral weight, so it has to be 35.

This doesnʼt work in the balanced ternary case, because 35 = 27 + 9 - 1, and without the 1 you could just tell it was less than 36 but more than 33, leaving 34 or 35.

[juliavixen]

The most efficient base for coding is actually about 2.71828... Euler's number. Though it has some practical difficulties with implementation.

The Soviet Union built some ternary computers in the 1960's. I think the US built a few too. It much easier to build and use a binary computer because the threshold for a bit error is higher. When you only have two possible voltages on a wire for zero and one, and there's some noise, or too much resistance in a switch, etc. the noise must be more than 50% of the voltage threshold to cause an error. In a ternary computer, the noise only needs to be more than 33% off from one of the three possible voltage values.

Also, it's easier to just switch something 100% on, or 100% off with a microscopic transistor that's just a few atoms of conductors and insulators stacked on top of each other.

Compact Discs are a 2.8MHz analog FM signal, from which an error-free 44.1KHz digital is produced. The entire point of using digital, binary, encoding is for signal to noise ratio. Shanon invented digital encoding for AT&T (Bell Labs) to eliminate the noise on long distance telephone calls. Continuous analog signals have lots of problems with noise, and the more symbols you add per signal event, the more and more your signal resembles analog again.

(Digital has ridiculously large bandwidth demands, but it is worth it to eliminate noise entirely.)

[adamswierczynski]

0:18 What happens when you put a bad apple on a teacher's desk.

[nicholasiverson]

Modal Ternary is the only way to go.
Having a system intrinsically treat the 0 1 or -1, 0 1 or 2, and 0 1 or !2.
!2 is the superposition state you see in quantum computers, where it will end up being 0 or 1 when read later for emulating a quantum system.
In addition to potentially higher density of data storage by 50%, there's interesting cases where you can compress data natively in a system like that, for example if you are storing a binary program you could include metadata with the 3rd component, or supermeta data with the mode on a trit by trit basis. Also can increase calculation speed for thirds, when binary is better at a calculation could just do it the old way.