- published: 23 Jun 2023
- views: 11585
Balanced ternary
Balanced ternary is a non-standard positional numeral system (a balanced form), useful for comparison logic. While it is a ternary (base 3) number system, in the standard (unbalanced) ternary system, digits have values 0, 1 and 2. The digits in the balanced ternary system have values −1, 0, and 1.
Different sources use different glyphs used to represent the three digits in balanced ternary. In this article, T (which resembles a ligature of the minus sign and 1) represents −1, while 0 and 1 represent themselves. Other conventions include using '−' and '+' to represent −1 and 1 respectively, or using Greek letter theta (Θ), which resembles a minus sign in a circle, to represent −1.
In Setun printings, −1 is represented as overturned 1: "1".
Computational properties
In the early days of computing, a few experimental Soviet computers were built with balanced ternary instead of binary, the most famous being the Setun, built by Nikolay Brusentsov and Sergei Sobolev. The notation has a number of computational advantages over regular binary. Particularly, the plus-minus consistency cuts down the carry rate in multi-digit multiplication, and the rounding-truncation equivalence cuts down the carry rate in rounding on fractions.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Balanced_ternary
Podcasts:
-
Counterfeit Coins and Balanced Ternary #SoME3
This video is part of the #SoME3 competition put on by @3blue1brown and @LeiosLabs . Here, we discuss a famous counterfeit coin weighing problem that asks us to find a counterfeit coin, and if it is heavier than or lighter than the rest, amongst 12 identical looking coins using a balance scale and three weighings. We present a classic, but not well known, solution using balanced ternary representations of numbers. This technique generalizes to more challenging, related problems, such as finding a counterfeit coin (and if it is heavier than or lighter than the rest) amongst 39 coins using exactly four weighings. We use visualizations to discuss the existence of balanced ternary representations and then explain how to actually solve the classic puzzle and the generalization to 39 coins....
published: 23 Jun 2023 -
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...
published: 08 May 2023 -
Mux in Logisim | Balanced Ternary Computer
published: 17 Feb 2020 -
Balanced Ternary Notation
http://demonstrations.wolfram.com/BalancedTernaryNotation The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. A number represented in binary is a sum of the powers of 2 (1, 2, 4, 8, 16, ...) multiplied by 0 or 1. For example, 60 in binary notation is 111100=1x32+1x16+1x8+1x4+0x2+0x1, using six "bits". Balanced ternary notation multiplies each power of 3 (1, 3, ... Contributed by: Ed Pegg Jr Audio created with WolframTones: http://tones.wolfram.com
published: 24 Jul 2017 -
Building A Base 3 Computer
Your computer uses ones and zeros to represent data. There's no real reason for be the basic unit of information in a computer to be only a one or zero, though. It's a historical choice that is common because of convention, like driving on one side of the road or having right-hand threads on bolts and screws. In fact, computers can be more efficient if they're built using different number systems. Base 3, or ternary, computing is more efficient at computation and actually makes the design of the computer easier. For the 2016 Hackaday Superconference, Jessie Tank gave a talk on what she's been working on for the past few years. It's a ternary computer, built with ones, zeros, and negative ones. This balanced ternary system is, 'Perhaps the prettiest number system of all,' writes Donald Knu...
published: 16 Dec 2016 -
IOTA tutorial 2.1: Convert decimal value to balanced ternary value
If you like this video and want to support me, go this page for my donation crypto addresses: https://www.youtube.com/c/mobilefish/about This is part 2.1 of the IOTA tutorial. In this video series different topics will be explained which will help you to understand IOTA. It is recommended to watch each video sequentially as I may refer to certain IOTA topics explained earlier. The trinary numeral system is often referred to as the ternary numeral system. The ternary (or trinary) numeral system has two types: The balanced ternary system in which a trit has the values: -1, 0 and 1. The unbalanced ternary system in which a trit has the values: 0, 1 and 2. When we speak of a base-3 numeral system we often refer to the unbalanced ternary system and not the balanced ternary system. In a bala...
published: 07 Dec 2017 -
Balanced Ternary System with Chinese Characters
This is the ternary system with Chinese characters used as numbers
published: 15 Jul 2023 -
Sekar bilgisayar chip 19 nedir -101
Kuran da chip ve yapay zeka. MÜDDESSİR 19 MESELESİ BİNARY ÇIKMAZI , VERİMSİZ CHIPLER HATALI BOOLEN LOJIC balanced ternary sekar
published: 25 Jul 2024 -
001: Balanced ternary inverter circuits
Positive/Negative/Symmetric ternary inverter circuits implemented with discrete components. Input signal is an O-P-O-N ternary square wave. #ternary #logicgate #electronics
published: 19 Oct 2021
13:11
Counterfeit Coins and Balanced Ternary #SoME3
- Order: Reorder
- Duration: 13:11
- Uploaded Date: 23 Jun 2023
- views: 11585
This video is part of the #SoME3 competition put on by @3blue1brown and @LeiosLabs . Here, we discuss a famous counterfeit coin weighing problem that asks us...
This video is part of the #SoME3 competition put on by @3blue1brown and @LeiosLabs . Here, we discuss a famous counterfeit coin weighing problem that asks us to find a counterfeit coin, and if it is heavier than or lighter than the rest, amongst 12 identical looking coins using a balance scale and three weighings. We present a classic, but not well known, solution using balanced ternary representations of numbers. This technique generalizes to more challenging, related problems, such as finding a counterfeit coin (and if it is heavier than or lighter than the rest) amongst 39 coins using exactly four weighings.
We use visualizations to discuss the existence of balanced ternary representations and then explain how to actually solve the classic puzzle and the generalization to 39 coins. If you feel up to it, perhaps you can devise the weighings to find a counterfeit coin (and if it is heavier than or lighter than the rest) amongst 120 coins using five weighings?
If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks!
The solution presented here can be found in various places, but one of my favorites is Bogomolny’s cut-the-knot site: https://www.cut-the-knot.org/blue/weight1.shtml
You can also check out this article that has a magic trick based on the 12-coin problem:
Balancing Magic with Mathematics by Tom Edgar in the April 2023 issue of Math Horizons (p. 20-23): https://doi.org/10.1080/10724117.2023.2168429
Here is an alternate solution to the twelve coin problem, but the solution feels unsatisfying to me: https://youtu.be/tE2dZLDJSjA
Here are other related articles if you are interested in balanced ternary:
Third Base by Brian Hayes in November/December 2001 Computing Science (p. 490-494): https://www.jstor.org/stable/27857554
The Goldilocks of Number Systems by Brian J. Shelburne in the April 2018 issue of Math Horizons (p 10-13): https://www.jstor.org/stable/48664205
#some3 #manim #balancedternary #numeralsystems #divisiontheorem #mathvideo #balancescale #scale #math #numbertheory #visualmath #visualproof #theorem #counterfeitcoin #logicpuzzle #weighing #weighingpuzzle #coinweighing
To learn more about animating with manim, check out:
https://manim.community
_____________________________
Music in this video:
The Dark Glow of the Mountains by Chris Zabriskie is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/by/4.0/
Source: http://chriszabriskie.com/darkglow/
Artist: http://chriszabriskie.com/
https://wn.com/Counterfeit_Coins_And_Balanced_Ternary_Some3
This video is part of the #SoME3 competition put on by @3blue1brown and @LeiosLabs . Here, we discuss a famous counterfeit coin weighing problem that asks us to find a counterfeit coin, and if it is heavier than or lighter than the rest, amongst 12 identical looking coins using a balance scale and three weighings. We present a classic, but not well known, solution using balanced ternary representations of numbers. This technique generalizes to more challenging, related problems, such as finding a counterfeit coin (and if it is heavier than or lighter than the rest) amongst 39 coins using exactly four weighings.
We use visualizations to discuss the existence of balanced ternary representations and then explain how to actually solve the classic puzzle and the generalization to 39 coins. If you feel up to it, perhaps you can devise the weighings to find a counterfeit coin (and if it is heavier than or lighter than the rest) amongst 120 coins using five weighings?
If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks!
The solution presented here can be found in various places, but one of my favorites is Bogomolny’s cut-the-knot site: https://www.cut-the-knot.org/blue/weight1.shtml
You can also check out this article that has a magic trick based on the 12-coin problem:
Balancing Magic with Mathematics by Tom Edgar in the April 2023 issue of Math Horizons (p. 20-23): https://doi.org/10.1080/10724117.2023.2168429
Here is an alternate solution to the twelve coin problem, but the solution feels unsatisfying to me: https://youtu.be/tE2dZLDJSjA
Here are other related articles if you are interested in balanced ternary:
Third Base by Brian Hayes in November/December 2001 Computing Science (p. 490-494): https://www.jstor.org/stable/27857554
The Goldilocks of Number Systems by Brian J. Shelburne in the April 2018 issue of Math Horizons (p 10-13): https://www.jstor.org/stable/48664205
#some3 #manim #balancedternary #numeralsystems #divisiontheorem #mathvideo #balancescale #scale #math #numbertheory #visualmath #visualproof #theorem #counterfeitcoin #logicpuzzle #weighing #weighingpuzzle #coinweighing
To learn more about animating with manim, check out:
https://manim.community
_____________________________
Music in this video:
The Dark Glow of the Mountains by Chris Zabriskie is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/by/4.0/
Source: http://chriszabriskie.com/darkglow/
Artist: http://chriszabriskie.com/
17:19
The Base Some Computers Use Instead of Binary
- Order: Reorder
- Duration: 17:19
- Uploaded Date: 08 May 2023
- views: 21923
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 puz...
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:
How to Count in Base Negative 10 - https://youtu.be/GWA_NraxOUw
How to Count in Fractional and Irrational Bases - https://www.youtube.com/watch?v=hI-pwt7LyUw
How to Count in Base 2i - https://youtu.be/MM0Sbfvf2Hw
Patterns Across the "Basic" Bases: https://youtu.be/qa8GuQLB7Wk
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:
Here's the newest one: https://youtube.com/shorts/Hk6sE9-M1mA?feature=share
Here's one about a geometric representation of the "difference of squares" identity: https://youtube.com/shorts/blqO-RaKrMI?feature=share
Here's one about the difference between 1/0 and 0/0: https://youtube.com/shorts/zhOiUNQtGF4?feature=share
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.
(To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at https://www.patreon.com/comboclass)
If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: https://youtu.be/_-gSvbvO8W4
Domotro
1442 A Walnut Street, Box # 401
Berkeley, CA 94709
Come chat with other combo lords on the Discord server here: https://discord.gg/cHHvDcPPuc
and there is a subreddit here: https://www.reddit.com/r/comboClass
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.
https://wn.com/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:
How to Count in Base Negative 10 - https://youtu.be/GWA_NraxOUw
How to Count in Fractional and Irrational Bases - https://www.youtube.com/watch?v=hI-pwt7LyUw
How to Count in Base 2i - https://youtu.be/MM0Sbfvf2Hw
Patterns Across the "Basic" Bases: https://youtu.be/qa8GuQLB7Wk
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:
Here's the newest one: https://youtube.com/shorts/Hk6sE9-M1mA?feature=share
Here's one about a geometric representation of the "difference of squares" identity: https://youtube.com/shorts/blqO-RaKrMI?feature=share
Here's one about the difference between 1/0 and 0/0: https://youtube.com/shorts/zhOiUNQtGF4?feature=share
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.
(To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at https://www.patreon.com/comboclass)
If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: https://youtu.be/_-gSvbvO8W4
Domotro
1442 A Walnut Street, Box # 401
Berkeley, CA 94709
Come chat with other combo lords on the Discord server here: https://discord.gg/cHHvDcPPuc
and there is a subreddit here: https://www.reddit.com/r/comboClass
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.
- published: 08 May 2023
- views: 21923
2:12
Mux in Logisim | Balanced Ternary Computer
- Order: Reorder
- Duration: 2:12
- Uploaded Date: 17 Feb 2020
- views: 1170
- published: 17 Feb 2020
- views: 1170
0:39
Balanced Ternary Notation
- Order: Reorder
- Duration: 0:39
- Uploaded Date: 24 Jul 2017
- views: 1139
http://demonstrations.wolfram.com/BalancedTernaryNotation
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new en...
http://demonstrations.wolfram.com/BalancedTernaryNotation
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A number represented in binary is a sum of the powers of 2 (1, 2, 4, 8, 16, ...) multiplied by 0 or 1. For example, 60 in binary notation is 111100=1x32+1x16+1x8+1x4+0x2+0x1, using six "bits". Balanced ternary notation multiplies each power of 3 (1, 3, ...
Contributed by: Ed Pegg Jr
Audio created with WolframTones:
http://tones.wolfram.com
https://wn.com/Balanced_Ternary_Notation
http://demonstrations.wolfram.com/BalancedTernaryNotation
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A number represented in binary is a sum of the powers of 2 (1, 2, 4, 8, 16, ...) multiplied by 0 or 1. For example, 60 in binary notation is 111100=1x32+1x16+1x8+1x4+0x2+0x1, using six "bits". Balanced ternary notation multiplies each power of 3 (1, 3, ...
Contributed by: Ed Pegg Jr
Audio created with WolframTones:
http://tones.wolfram.com
- published: 24 Jul 2017
- views: 1139
20:24
Building A Base 3 Computer
- Order: Reorder
- Duration: 20:24
- Uploaded Date: 16 Dec 2016
- views: 37402
Your computer uses ones and zeros to represent data. There's no real reason for be the basic unit of information in a computer to be only a one or zero, though....
Your computer uses ones and zeros to represent data. There's no real reason for be the basic unit of information in a computer to be only a one or zero, though. It's a historical choice that is common because of convention, like driving on one side of the road or having right-hand threads on bolts and screws. In fact, computers can be more efficient if they're built using different number systems. Base 3, or ternary, computing is more efficient at computation and actually makes the design of the computer easier.
For the 2016 Hackaday Superconference, Jessie Tank gave a talk on what she's been working on for the past few years. It's a ternary computer, built with ones, zeros, and negative ones. This balanced ternary system is, 'Perhaps the prettiest number system of all,' writes Donald Knuth, and now this number system has made it into silicon as a real microprocessor.
Read the article:
http://hackaday.com/?p=235852
Learn about the Hackaday SuperConference:
https://hackaday.io/superconference/
https://wn.com/Building_A_Base_3_Computer
Your computer uses ones and zeros to represent data. There's no real reason for be the basic unit of information in a computer to be only a one or zero, though. It's a historical choice that is common because of convention, like driving on one side of the road or having right-hand threads on bolts and screws. In fact, computers can be more efficient if they're built using different number systems. Base 3, or ternary, computing is more efficient at computation and actually makes the design of the computer easier.
For the 2016 Hackaday Superconference, Jessie Tank gave a talk on what she's been working on for the past few years. It's a ternary computer, built with ones, zeros, and negative ones. This balanced ternary system is, 'Perhaps the prettiest number system of all,' writes Donald Knuth, and now this number system has made it into silicon as a real microprocessor.
Read the article:
http://hackaday.com/?p=235852
Learn about the Hackaday SuperConference:
https://hackaday.io/superconference/
- published: 16 Dec 2016
- views: 37402
14:11
IOTA tutorial 2.1: Convert decimal value to balanced ternary value
- Order: Reorder
- Duration: 14:11
- Uploaded Date: 07 Dec 2017
- views: 11704
If you like this video and want to support me, go this page for my donation crypto addresses:
https://www.youtube.com/c/mobilefish/about
This is part 2.1 of th...
If you like this video and want to support me, go this page for my donation crypto addresses:
https://www.youtube.com/c/mobilefish/about
This is part 2.1 of the IOTA tutorial.
In this video series different topics will be explained which will help you to understand IOTA.
It is recommended to watch each video sequentially as I may refer to certain IOTA topics explained earlier.
The trinary numeral system is often referred to as the ternary numeral system.
The ternary (or trinary) numeral system has two types:
The balanced ternary system in which a trit has the values: -1, 0 and 1.
The unbalanced ternary system in which a trit has the values: 0, 1 and 2.
When we speak of a base-3 numeral system we often refer to the unbalanced ternary system and not the balanced ternary system.
In a balanced ternary system, instead of using the values -1, 0 and 1 we can use other symbols, such as the letter T, 0 and 1 or the minus sign (-), 0 and the plus sign (+).
For example a balanced ternary value can be written as: 1-110-1 = 1T10T = +-+0-
When converting any base-N number to a decimal number, remember that the most left value is the most significant value and the most right value is the least significant value.
Convert a base-2 value (binary value) to a decimal value = 1101 (bin) = 1 x 2^3 + 1 x 2^2 + 0 x 2^1 + 1 x 2^0 = 13 (dec)
Convert a base-3 value (unbalanced ternary value) to a decimal value =2101 (ternary) = 2 x 3^3 + 1 x 3^2 + 0 x 3^1 + 1 x 3^0 = 64 (dec)
Convert a base-10 value (decimal value) to a decimal value =6389 (dec) = 6 x 10^3 + 3 x 10^2 + 8 x 10^1 + 9 x 10^0 = 6389 (dec)
To convert a decimal value to a balanced ternary value is a two step process.
Step 1: Convert the decimal value to a base-3 or unbalanced ternary value:
https://www.mobilefish.com/download/iota/convert_decimal_to_base3_example1.txt
https://www.mobilefish.com/download/iota/convert_decimal_to_base3_example2.txt
Step 2: Convert the base-3 value to a balanced ternary value.
https://www.mobilefish.com/download/iota/convert_base3_to_balanced_ternary.txt
Check out all my other IOTA tutorial videos
https://goo.gl/aNHf1y
Subscribe to my YouTube channel:
https://goo.gl/61NFzK
The presentation used in this video tutorial can be found at:
https://www.mobilefish.com/developer/iota/iota_quickguide_tutorial.html
#mobilefish #howto #iota
https://wn.com/Iota_Tutorial_2.1_Convert_Decimal_Value_To_Balanced_Ternary_Value
If you like this video and want to support me, go this page for my donation crypto addresses:
https://www.youtube.com/c/mobilefish/about
This is part 2.1 of the IOTA tutorial.
In this video series different topics will be explained which will help you to understand IOTA.
It is recommended to watch each video sequentially as I may refer to certain IOTA topics explained earlier.
The trinary numeral system is often referred to as the ternary numeral system.
The ternary (or trinary) numeral system has two types:
The balanced ternary system in which a trit has the values: -1, 0 and 1.
The unbalanced ternary system in which a trit has the values: 0, 1 and 2.
When we speak of a base-3 numeral system we often refer to the unbalanced ternary system and not the balanced ternary system.
In a balanced ternary system, instead of using the values -1, 0 and 1 we can use other symbols, such as the letter T, 0 and 1 or the minus sign (-), 0 and the plus sign (+).
For example a balanced ternary value can be written as: 1-110-1 = 1T10T = +-+0-
When converting any base-N number to a decimal number, remember that the most left value is the most significant value and the most right value is the least significant value.
Convert a base-2 value (binary value) to a decimal value = 1101 (bin) = 1 x 2^3 + 1 x 2^2 + 0 x 2^1 + 1 x 2^0 = 13 (dec)
Convert a base-3 value (unbalanced ternary value) to a decimal value =2101 (ternary) = 2 x 3^3 + 1 x 3^2 + 0 x 3^1 + 1 x 3^0 = 64 (dec)
Convert a base-10 value (decimal value) to a decimal value =6389 (dec) = 6 x 10^3 + 3 x 10^2 + 8 x 10^1 + 9 x 10^0 = 6389 (dec)
To convert a decimal value to a balanced ternary value is a two step process.
Step 1: Convert the decimal value to a base-3 or unbalanced ternary value:
https://www.mobilefish.com/download/iota/convert_decimal_to_base3_example1.txt
https://www.mobilefish.com/download/iota/convert_decimal_to_base3_example2.txt
Step 2: Convert the base-3 value to a balanced ternary value.
https://www.mobilefish.com/download/iota/convert_base3_to_balanced_ternary.txt
Check out all my other IOTA tutorial videos
https://goo.gl/aNHf1y
Subscribe to my YouTube channel:
https://goo.gl/61NFzK
The presentation used in this video tutorial can be found at:
https://www.mobilefish.com/developer/iota/iota_quickguide_tutorial.html
#mobilefish #howto #iota
- published: 07 Dec 2017
- views: 11704
5:57
Balanced Ternary System with Chinese Characters
- Order: Reorder
- Duration: 5:57
- Uploaded Date: 15 Jul 2023
- views: 189
This is the ternary system with Chinese characters used as numbers
This is the ternary system with Chinese characters used as numbers
https://wn.com/Balanced_Ternary_System_With_Chinese_Characters
This is the ternary system with Chinese characters used as numbers
- published: 15 Jul 2023
- views: 189
9:15
Sekar bilgisayar chip 19 nedir -101
- Order: Reorder
- Duration: 9:15
- Uploaded Date: 25 Jul 2024
- views: 175
Kuran da chip ve yapay zeka. MÜDDESSİR
19 MESELESİ
BİNARY ÇIKMAZI , VERİMSİZ CHIPLER HATALI BOOLEN LOJIC
balanced ternary sekar
Kuran da chip ve yapay zeka. MÜDDESSİR
19 MESELESİ
BİNARY ÇIKMAZI , VERİMSİZ CHIPLER HATALI BOOLEN LOJIC
balanced ternary sekar
https://wn.com/Sekar_Bilgisayar_Chip_19_Nedir_101
Kuran da chip ve yapay zeka. MÜDDESSİR
19 MESELESİ
BİNARY ÇIKMAZI , VERİMSİZ CHIPLER HATALI BOOLEN LOJIC
balanced ternary sekar
- published: 25 Jul 2024
- views: 175
0:31
001: Balanced ternary inverter circuits
- Order: Reorder
- Duration: 0:31
- Uploaded Date: 19 Oct 2021
- views: 542
Positive/Negative/Symmetric ternary inverter circuits implemented with discrete components.
Input signal is an O-P-O-N ternary square wave.
#ternary #logicg...
Positive/Negative/Symmetric ternary inverter circuits implemented with discrete components.
Input signal is an O-P-O-N ternary square wave.
#ternary #logicgate #electronics
https://wn.com/001_Balanced_Ternary_Inverter_Circuits
Positive/Negative/Symmetric ternary inverter circuits implemented with discrete components.
Input signal is an O-P-O-N ternary square wave.
#ternary #logicgate #electronics
- published: 19 Oct 2021
- views: 542
PLAYLIST TIME:
PLAYLIST TIME:
13:11
Counterfeit Coins and Balanced Ternary #SoME3
This video is part of the #SoME3 competition put on by @3blue1brown and @LeiosLabs . He...
published: 23 Jun 2023
Counterfeit Coins and Balanced Ternary #SoME3
Counterfeit Coins and Balanced Ternary #SoME3
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- published: 23 Jun 2023
- views: 11585
This video is part of the #SoME3 competition put on by @3blue1brown and @LeiosLabs . Here, we discuss a famous counterfeit coin weighing problem that asks us to find a counterfeit coin, and if it is heavier than or lighter than the rest, amongst 12 identical looking coins using a balance scale and three weighings. We present a classic, but not well known, solution using balanced ternary representations of numbers. This technique generalizes to more challenging, related problems, such as finding a counterfeit coin (and if it is heavier than or lighter than the rest) amongst 39 coins using exactly four weighings.
We use visualizations to discuss the existence of balanced ternary representations and then explain how to actually solve the classic puzzle and the generalization to 39 coins. If you feel up to it, perhaps you can devise the weighings to find a counterfeit coin (and if it is heavier than or lighter than the rest) amongst 120 coins using five weighings?
If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks!
The solution presented here can be found in various places, but one of my favorites is Bogomolny’s cut-the-knot site: https://www.cut-the-knot.org/blue/weight1.shtml
You can also check out this article that has a magic trick based on the 12-coin problem:
Balancing Magic with Mathematics by Tom Edgar in the April 2023 issue of Math Horizons (p. 20-23): https://doi.org/10.1080/10724117.2023.2168429
Here is an alternate solution to the twelve coin problem, but the solution feels unsatisfying to me: https://youtu.be/tE2dZLDJSjA
Here are other related articles if you are interested in balanced ternary:
Third Base by Brian Hayes in November/December 2001 Computing Science (p. 490-494): https://www.jstor.org/stable/27857554
The Goldilocks of Number Systems by Brian J. Shelburne in the April 2018 issue of Math Horizons (p 10-13): https://www.jstor.org/stable/48664205
#some3 #manim #balancedternary #numeralsystems #divisiontheorem #mathvideo #balancescale #scale #math #numbertheory #visualmath #visualproof #theorem #counterfeitcoin #logicpuzzle #weighing #weighingpuzzle #coinweighing
To learn more about animating with manim, check out:
https://manim.community
_____________________________
Music in this video:
The Dark Glow of the Mountains by Chris Zabriskie is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/by/4.0/
Source: http://chriszabriskie.com/darkglow/
Artist: http://chriszabriskie.com/
17:19
The Base Some Computers Use Instead of Binary
Most computers use binary, but some actually use a lesser-known base called "balanced tern...
published: 08 May 2023
The Base Some Computers Use Instead of Binary
The Base Some Computers Use Instead of Binary
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- published: 08 May 2023
- views: 21923
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:
How to Count in Base Negative 10 - https://youtu.be/GWA_NraxOUw
How to Count in Fractional and Irrational Bases - https://www.youtube.com/watch?v=hI-pwt7LyUw
How to Count in Base 2i - https://youtu.be/MM0Sbfvf2Hw
Patterns Across the "Basic" Bases: https://youtu.be/qa8GuQLB7Wk
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:
Here's the newest one: https://youtube.com/shorts/Hk6sE9-M1mA?feature=share
Here's one about a geometric representation of the "difference of squares" identity: https://youtube.com/shorts/blqO-RaKrMI?feature=share
Here's one about the difference between 1/0 and 0/0: https://youtube.com/shorts/zhOiUNQtGF4?feature=share
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.
(To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at https://www.patreon.com/comboclass)
If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: https://youtu.be/_-gSvbvO8W4
Domotro
1442 A Walnut Street, Box # 401
Berkeley, CA 94709
Come chat with other combo lords on the Discord server here: https://discord.gg/cHHvDcPPuc
and there is a subreddit here: https://www.reddit.com/r/comboClass
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.
2:12
Mux in Logisim | Balanced Ternary Computer
published: 17 Feb 2020
Mux in Logisim | Balanced Ternary Computer
Mux in Logisim | Balanced Ternary Computer
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- published: 17 Feb 2020
- views: 1170
0:39
Balanced Ternary Notation
http://demonstrations.wolfram.com/BalancedTernaryNotation
The Wolfram Demonstrations Proj...
published: 24 Jul 2017
Balanced Ternary Notation
Balanced Ternary Notation
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- published: 24 Jul 2017
- views: 1139
http://demonstrations.wolfram.com/BalancedTernaryNotation
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A number represented in binary is a sum of the powers of 2 (1, 2, 4, 8, 16, ...) multiplied by 0 or 1. For example, 60 in binary notation is 111100=1x32+1x16+1x8+1x4+0x2+0x1, using six "bits". Balanced ternary notation multiplies each power of 3 (1, 3, ...
Contributed by: Ed Pegg Jr
Audio created with WolframTones:
http://tones.wolfram.com
20:24
Building A Base 3 Computer
Your computer uses ones and zeros to represent data. There's no real reason for be the bas...
published: 16 Dec 2016
Building A Base 3 Computer
Building A Base 3 Computer
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- published: 16 Dec 2016
- views: 37402
Your computer uses ones and zeros to represent data. There's no real reason for be the basic unit of information in a computer to be only a one or zero, though. It's a historical choice that is common because of convention, like driving on one side of the road or having right-hand threads on bolts and screws. In fact, computers can be more efficient if they're built using different number systems. Base 3, or ternary, computing is more efficient at computation and actually makes the design of the computer easier.
For the 2016 Hackaday Superconference, Jessie Tank gave a talk on what she's been working on for the past few years. It's a ternary computer, built with ones, zeros, and negative ones. This balanced ternary system is, 'Perhaps the prettiest number system of all,' writes Donald Knuth, and now this number system has made it into silicon as a real microprocessor.
Read the article:
http://hackaday.com/?p=235852
Learn about the Hackaday SuperConference:
https://hackaday.io/superconference/
14:11
IOTA tutorial 2.1: Convert decimal value to balanced ternary value
If you like this video and want to support me, go this page for my donation crypto address...
published: 07 Dec 2017
IOTA tutorial 2.1: Convert decimal value to balanced ternary value
IOTA tutorial 2.1: Convert decimal value to balanced ternary value
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- published: 07 Dec 2017
- views: 11704
If you like this video and want to support me, go this page for my donation crypto addresses:
https://www.youtube.com/c/mobilefish/about
This is part 2.1 of the IOTA tutorial.
In this video series different topics will be explained which will help you to understand IOTA.
It is recommended to watch each video sequentially as I may refer to certain IOTA topics explained earlier.
The trinary numeral system is often referred to as the ternary numeral system.
The ternary (or trinary) numeral system has two types:
The balanced ternary system in which a trit has the values: -1, 0 and 1.
The unbalanced ternary system in which a trit has the values: 0, 1 and 2.
When we speak of a base-3 numeral system we often refer to the unbalanced ternary system and not the balanced ternary system.
In a balanced ternary system, instead of using the values -1, 0 and 1 we can use other symbols, such as the letter T, 0 and 1 or the minus sign (-), 0 and the plus sign (+).
For example a balanced ternary value can be written as: 1-110-1 = 1T10T = +-+0-
When converting any base-N number to a decimal number, remember that the most left value is the most significant value and the most right value is the least significant value.
Convert a base-2 value (binary value) to a decimal value = 1101 (bin) = 1 x 2^3 + 1 x 2^2 + 0 x 2^1 + 1 x 2^0 = 13 (dec)
Convert a base-3 value (unbalanced ternary value) to a decimal value =2101 (ternary) = 2 x 3^3 + 1 x 3^2 + 0 x 3^1 + 1 x 3^0 = 64 (dec)
Convert a base-10 value (decimal value) to a decimal value =6389 (dec) = 6 x 10^3 + 3 x 10^2 + 8 x 10^1 + 9 x 10^0 = 6389 (dec)
To convert a decimal value to a balanced ternary value is a two step process.
Step 1: Convert the decimal value to a base-3 or unbalanced ternary value:
https://www.mobilefish.com/download/iota/convert_decimal_to_base3_example1.txt
https://www.mobilefish.com/download/iota/convert_decimal_to_base3_example2.txt
Step 2: Convert the base-3 value to a balanced ternary value.
https://www.mobilefish.com/download/iota/convert_base3_to_balanced_ternary.txt
Check out all my other IOTA tutorial videos
https://goo.gl/aNHf1y
Subscribe to my YouTube channel:
https://goo.gl/61NFzK
The presentation used in this video tutorial can be found at:
https://www.mobilefish.com/developer/iota/iota_quickguide_tutorial.html
#mobilefish #howto #iota
5:57
Balanced Ternary System with Chinese Characters
This is the ternary system with Chinese characters used as numbers
published: 15 Jul 2023
Balanced Ternary System with Chinese Characters
Balanced Ternary System with Chinese Characters
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- published: 15 Jul 2023
- views: 189
This is the ternary system with Chinese characters used as numbers
9:15
Sekar bilgisayar chip 19 nedir -101
Kuran da chip ve yapay zeka. MÜDDESSİR
19 MESELESİ
BİNARY ÇIKMAZI , VERİMSİZ CHIPLER ...
published: 25 Jul 2024
Sekar bilgisayar chip 19 nedir -101
Sekar bilgisayar chip 19 nedir -101
- Report rights infringement
- published: 25 Jul 2024
- views: 175
Kuran da chip ve yapay zeka. MÜDDESSİR
19 MESELESİ
BİNARY ÇIKMAZI , VERİMSİZ CHIPLER HATALI BOOLEN LOJIC
balanced ternary sekar
0:31
001: Balanced ternary inverter circuits
Positive/Negative/Symmetric ternary inverter circuits implemented with discrete components...
published: 19 Oct 2021
001: Balanced ternary inverter circuits
001: Balanced ternary inverter circuits
- Report rights infringement
- published: 19 Oct 2021
- views: 542
Positive/Negative/Symmetric ternary inverter circuits implemented with discrete components.
Input signal is an O-P-O-N ternary square wave.
#ternary #logicgate #electronics
Balanced ternary
Balanced ternary is a non-standard positional numeral system (a balanced form), useful for comparison logic. While it is a ternary (base 3) number system, in the standard (unbalanced) ternary system, digits have values 0, 1 and 2. The digits in the balanced ternary system have values −1, 0, and 1.
Different sources use different glyphs used to represent the three digits in balanced ternary. In this article, T (which resembles a ligature of the minus sign and 1) represents −1, while 0 and 1 represent themselves. Other conventions include using '−' and '+' to represent −1 and 1 respectively, or using Greek letter theta (Θ), which resembles a minus sign in a circle, to represent −1.
In Setun printings, −1 is represented as overturned 1: "1".
Computational properties
In the early days of computing, a few experimental Soviet computers were built with balanced ternary instead of binary, the most famous being the Setun, built by Nikolay Brusentsov and Sergei Sobolev. The notation has a number of computational advantages over regular binary. Particularly, the plus-minus consistency cuts down the carry rate in multi-digit multiplication, and the rounding-truncation equivalence cuts down the carry rate in rounding on fractions.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Balanced_ternary
Counterfeit Coins and Balanced Ternary #SoME3...
The Base Some Computers Use Instead of Binary...
Mux in Logisim | Balanced Ternary Computer...
Balanced Ternary Notation...
Building A Base 3 Computer...
IOTA tutorial 2.1: Convert decimal value to balanc...
Balanced Ternary System with Chinese Characters...
Sekar bilgisayar chip 19 nedir -101...