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What's wrong with larger than binary code? (Base 4?) - Page 2

post #41 of 69
[quote]Originally posted by 123:
<strong>
Runtimes for problems in P are O(n) = constant, O(n^2), O(n^10000), and any O(n^k) = polynomial time.
</strong><hr></blockquote>

Just a slight nitpick: Constant run time is O(1), not O(n).

Bye,
RazzFazz
post #42 of 69
There's one simple thing you guys don't seem to understand. Have you ever been able to compare 3 things at the same time? It's impossible. You've got to figure out couples to do this.
So this is the same with computers, or logics. Thins can only be compared by pairs.
That's why everything is binary today (and will be tomorrow)
post #43 of 69
Quantum computers compare all options at the same time.

Yes they only have 2 states, but the fact that they can hold these 2 states at the same time is important. That means while a single switch (qubit) can only have 2 options, a 2 qubit computer has 4 options, a 3 qubit has 8, and..

4 qubit = 16 switches
5 qubit = 32 switches
6 qubit = 64 switches
7 qubit = 128 switches
8 qubit = 256 switches
...
41 qubit computer = 4,398,046,511,104 switches

You can see that once we get into the several hundred qubit range, we get computation that far exceeds ALL ther current computers in the world.

We'll be able to easily replicate the trillions of connections and billions of neurons in the human brain.

All this is dependent on our ability to sink money into pure research and space exploration. I'm just glad India, China, UK, and Japan continue to invest... Too bad for the greedy Romans.. I mean the US..he he (just joking for the PC crowd)

[ 08-01-2002: Message edited by: JasonPP ]</p>
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post #44 of 69
[quote]Originally posted by Eupfhoria:
<strong>For all of you enlighened people here, why couldn't a company move to say Base 4 code rather than base 2?

Concievably it wouldn't be that tough for wiring to be accurate enough to support 4 levels of light/eletricity intensity, plus base 4 will save alot of space when considering a HD.
(Considering DNA uses base 4 with its ATCG codes)

I'm asking, what is the probability of this happening in the future (yeah, we'll prolly get yetaherz G28s first, but....)</strong><hr></blockquote>

First, you'd need greater than base four binary numbers to code all of the DNA sequences.

Second, it will never happen. It is impossible for a computer to be presented with a situation with three possible answers simultaneously. For example, a computer and a person are presented with three stones marked 7, 8, and 9. Both the human and the computer are asked to pick the middle value. Of course the human immediately picks up the 8 as the middle value, whereas the computer first compares 7 to 8, realizes 8 is greater, and then 8 to 9 and realizes 9 is greater. It arrives at the logical conclusion that 8 must be the middle value since it is greater than 7 and less than 9. Now the human might say that he immediately recognized 8 as the middle number, but the human logically deduced that 8 is the middle number, being trained in a sequence of numbers that 8 is greater than 7 and less than 9. If there are three choices (or more for the answer), the computer must go through and check all of them to get the right value. Now, this can be solved easier with some algorithms. For example, lots of time can be saved if the data is sorted in some manner.

I don't think we'll see any major breakthroughs in chip fabrication until they implement superconducting semiconductors (how's that for an oxymoron) in processors. It would solve a lot of the heat problems. Also, I think they'll probably move towards asynchronous CPU's, where the only delays are the gate delays instead of waiting for the clock for something to happen.

[ 08-01-2002: Message edited by: Majuki ]</p>
post #45 of 69
First of all, electromagnetic-based Base 4 computers already exist as prototypes (e.g. at the CNET or at the ENSTA in France), but developments around this technology have almost ceased: true, such computers were blazingly fast, but they were extremely buggy (even more buggy than some of the attempts in the lands of quantum computing!).
And that's the main quality of Base 2 components: they are stable! Errors made by such components are marginal, since they only have two remarkable values: a zero value, and a peak value (by comparison, admit that it is quite easy to guess if you are on the top of mount everest or if you are at the level of the sea). Base 4 components have 4 remarkable values: pretty tough to guess if you are on the top of mount everest, the top of mount kilimandjaro, the top of mount white, or the level of the sea... the error marginal in such components are therefore higher...
Anyway, for people who care about that, Base 10 computers are under development at the CNET of Lannion, in France. They're based on electromagnetical wavelenght recognition (color recognition, for the ones who did not understand!!! ) but currently, the "micro"processor occupies a whole 100 meters square, while being 4 meters high! Engineers at Lannion say that Base 10 computers might start getting sold by 2010-2012!

Well, guys, that's all i had to say about this topic! thx for having read me!

Cheers! <img src="graemlins/smokin.gif" border="0" alt="[Chilling]" />
post #46 of 69
[quote]Originally posted by evangellydonut:
<strong>

lol I have a poorly coded program in LISP that "tries" to do this...turned out pretty damn inefficient though ^_^; that's why i'm not a CS major I guess...</strong><hr></blockquote>

My offhand guess is that your run time would be n^3*log(n). This means that 100 locations runs something like 1000 times slower than 10 locations. (give or take some nasty constants that make quite a difference when your run time is already going to be so large).

[ 08-01-2002: Message edited by: Yevgeny ]</p>
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post #47 of 69
[quote]Originally posted by MrBillData:
<strong>This is all so very confusing.

How about One's complement bits.

You have 1, 0, and -0. <img src="graemlins/lol.gif" border="0" alt="[Laughing]" />

Tri-Logic Test:
0 OR -0 = ?
1 AND -0 = ?
</strong><hr></blockquote>


Actually, you can generate -0 pretty easily in a normal machine. One of my coworkers had a bug (curiously, in a product that solves the TSP is record time) where he was bitshifting a bit and managed to shift the bit all the way up to the sign bit. The end result was to produce the odd comparison where the CPU rightly said that 0 != -0. Took a couple of days to find this bug...

For those ofyou who think that machines are going to become intelligent and take over the world, take a few programming classes so that you can get a good dose of reality. <img src="graemlins/oyvey.gif" border="0" alt="[No]" />
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post #48 of 69
[quote]Originally posted by JasonPP:
<strong>

You can see that once we get into the several hundred qubit range, we get computation that far exceeds ALL ther current computers in the world.

We'll be able to easily replicate the trillions of connections and billions of neurons in the human brain.

All this is dependent on our ability to sink money into pure research and space exploration. I'm just glad India, China, UK, and Japan continue to invest... Too bad for the greedy Romans.. I mean the US..he he (just joking for the PC crowd)

[ 08-01-2002: Message edited by: JasonPP ]</strong><hr></blockquote>

Different computers have different tradeoffs. For example, a natural computer (filing cabinet) can insert into a list in O(1) time, where a computer can only insert into a list in O(n) time. A natural computer can actually find a path in O(1) time, where a computer generally can't do better than O(n log(n)) time. My guess is that quantum computers aren't all cake and ice cream and they too have their limitations (if not just in the general difficulty in programming them).

As for the troll ending, you are obviously not a person who reads much at the end of articles about quantum computing. For example, the primary places in which research into quantum computing is happening are in America. Why you ask? Well, read the articles to see who is funding IBM and varous universities to get this funding- all the funds come from the department of defense who want to use quantum computing for cryptography purposes. Quantum computing is very heavily researched in the States, and for pretty obvious reasons.

As for the state of R&D investment in the world, get a clue. America does invest quite a bit.
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post #49 of 69
Take a minute and think of today. How many machines have you interfaced with or used the products of?

Machines have already "taken over". No one wants to admit it though.. It's not neccisarily a bad thing either..

Regarding my troll, I understnad that the US continues to contribute a lot to pure research, all I was refering to was the current "administration" and their historical record of limiting non-military pure research. Oil interests seem to be more important. It's frustrating to scientists in the US. My first read on quantum computing was in fact the IBM research.

I'm not anti-US, I'm pro-sustainable development.
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post #50 of 69
[quote]Originally posted by Yevgeny:
<strong>
Actually, you can generate -0 pretty easily in a normal machine. One of my coworkers had a bug (curiously, in a product that solves the TSP is record time) where he was bitshifting a bit and managed to shift the bit all the way up to the sign bit. The end result was to produce the odd comparison where the CPU rightly said that 0 != -0. Took a couple of days to find this bug...
</strong><hr></blockquote>

Unless your co-worker was bit-shifting floats, he must have been using a pretty non-standard computer in order to be able to get a "-0" result - at least I don't know of any current computer architecture that does not use two's complement representation for negative integer numbers, and there is no "-0" in two's complement representation (i.e. "10000000" is "-128", not "-0").

Bye,
RazzFazz

[ 08-01-2002: Message edited by: RazzFazz ]</p>
post #51 of 69
[quote]Originally posted by JasonPP:
<strong>Take a minute and think of today. How many machines have you interfaced with or used the products of?

Machines have already "taken over". No one wants to admit it though.. It's not neccisarily a bad thing either..

Regarding my troll, I understnad that the US continues to contribute a lot to pure research, all I was refering to was the current "administration" and their historical record of limiting non-military pure research. Oil interests seem to be more important. It's frustrating to scientists in the US. My first read on quantum computing was in fact the IBM research.

I'm not anti-US, I'm pro-sustainable development.</strong><hr></blockquote>

My bad for misunderstanding what you meant by research.

Actually, I have an interesting story for you. A few years ago, I returned to my alma mater to attend a friend's graduation. At my college, computer science grads have the same ceremony with physical science grads. Every year, the speaker is chosen from the other school, and this year, we had the president and CEO of Orange County Teachers Federal Credit Union (a famos researcher turned businessman). So this guy got up on the stage and actually decried the lack of R&D funds in society. Why the sudden lack of funding? Well, he said it was because the cold war ended. I never thought I would see someone pining away for the return of the cold war, but this guy was doing it. Military R&D does translate directly to normal R&D, in fact this is one of the reasons why some large $ value projects are undertaken. It is a sad fact about humans that militarism has always been the prime motivator for technological advancement.

Although I supose that nowadays, it is militarism and greed that is the basis for R&D.

P.S. The previous adminsitration killed off big science too (remember the big suerconductor that was being built in Texas?).
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post #52 of 69
[quote]Originally posted by Yevgeny:
<strong>For those ofyou who think that machines are going to become intelligent and take over the world, take a few programming classes so that you can get a good dose of reality. <img src="graemlins/oyvey.gif" border="0" alt="[No]" /> </strong><hr></blockquote>

Butbutbut! Didn't you see (scary voice on) The Matrix (scary voice off)?

Teehee!
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post #53 of 69
[quote]Originally posted by xype:
<strong>

Butbutbut! Didn't you see (scary voice on) The Matrix (scary voice off)?

Teehee!</strong><hr></blockquote>

"The Matrix is everywhere, it's all around us, here even in this room. You can see it out your window, or on your television. You feel it when you go to work, or go to church or pay your taxes. It is the world that has been pulled over your eyes to blind you from the truth."

iMatrix by Apple Computer, coming to a world near you. <img src="graemlins/lol.gif" border="0" alt="[Laughing]" /> <img src="graemlins/lol.gif" border="0" alt="[Laughing]" /> <img src="graemlins/lol.gif" border="0" alt="[Laughing]" />
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post #54 of 69
[quote]Originally posted by Yevgeny:
<strong>

P.S. The previous adminsitration killed off big science too (remember the big suerconductor that was being built in Texas?).</strong><hr></blockquote>

You mean the supercollider. It was supposed to be the biggest partical accelerator in the world and allow physicists to delve ever deeper into the realms of subparticals. Looks like the one at FermiLab and CERN will have to do for another 20 years. Government spending at non-military national laboratories has been very weak. All the benefits of the big spending in the space program have evaporated. Its amazing that the budget increase each year for defense is more than the entirity of what NASA gets.
Research on quantum computing will come from the private sector. IBM has been a big name in quantum computing for a long time now, i've read a lot about what they're doing. Michael Crichtons book Timeline has some interesting info on quantum computing. Its fiction, but just like Jurassic Park he does a very good job of researching his topics beforehand. Sort of applying science fact to an interesting plot.
Anyway thats my two bits, quantum computing is a very real thing, and definitely the next big push. But just like oil and car companies, computer companies aren't going to invest major research dollars until the silicon well runs dry.
I've always thought Intel and AMD were in collusion. Cranking out just decent chips. Think about it, if Intel puts AMD out of business by putting out something too fast or revolutionary, antitrust all the way to the bank. Also, if consumers and businesses will buy a slightly faster chip why make something that blows everyone away. Another speculation, just about as far fetched as the former, is that maybe the government doesn't want a quantum chip out for the public just yet. It could crack any known encryption, also we wouldn't want it to get in the wrong hands.
Anywho thats it from here. Just a thought.
post #55 of 69
[quote]Originally posted by smashingym:
<strong>[...]It could crack any known encryption, [...]</strong><hr></blockquote>

Except for Quantum Encryption, which IIRC is uncrackable.
post #56 of 69
[quote]Originally posted by Whisper:
<strong>

Except for Quantum Encryption, which IIRC is uncrackable.</strong><hr></blockquote>

Uncrackable... maybe,
impractical... definitly.

Long distance Quantum Encryption will never be practical and I suspect can't work for exoatmospheric communications.
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post #57 of 69
[quote]Originally posted by smashingym:
[QB]


I've always thought Intel and AMD were in collusion. Cranking out just decent chips. Think about it, if Intel puts AMD out of business by putting out something too fast or revolutionary, antitrust all the way to the bank. [QB]<hr></blockquote>

Intel has been trying to put AMD out of business for the past 15 years or so, ever since AMD had the gaul to try to enter the microprocessor business which Intel regards as their exclusive domain. And some would argue that Intel has used monopolistic practices to ensure they remain the dominant producer of microprocessors in the world.
post #58 of 69
[quote]Originally posted by RazzFazz:
<strong>

Just a slight nitpick: Constant run time is O(1), not O(n).

Bye,
RazzFazz</strong><hr></blockquote>

O(n) is of course linear and not constant.
post #59 of 69
[quote]Originally posted by Yevgeny:
<strong>

where a computer can only insert into a list in O(n) time. </strong><hr></blockquote>

Unsorted list insert is O(1). Sorted lists are implemented as trees and have O(log n) time complexity for insert operations.

123
post #60 of 69
Very Interesting, although the complexity grows exponentially with such an idea.

So I'd gather, the input signals are fed through some sort of voltage comparators and depending upon the gate, it makes a a voltage decision (output)

Using 0,1,2,3 look at what you get:

000 002 003 112 113 323
001 022 033 122 133 223
011 222 333 121 333 233
111 220 330 221 331 333
110 200 300 211 311 332
100 202 303 212 313 322
101 020 030 131 232
010

42 combinations over 8 combinations with just base2 (unless I made some mistakes) 80% More!
post #61 of 69
Thread Starter 
[quote]Originally posted by MajorMatt:
<strong>Very Interesting, although the complexity grows exponentially with such an idea.

So I'd gather, the input signals are fed through some sort of voltage comparators and depending upon the gate, it makes a a voltage decision (output)

Using 0,1,2,3 look at what you get:

000 002 003 112 113 323
001 022 033 122 133 223
011 222 333 121 333 233
111 220 330 221 331 333
110 200 300 211 311 332
100 202 303 212 313 322
101 020 030 131 232
010

42 combinations over 8 combinations with just base2 (unless I made some mistakes) 80% More!</strong><hr></blockquote>
Yeah, you missed a bunch

000 002 003 112 113 323 132 102
001 022 033 122 133 223 321 120
011 222 333 121 333 233 312 210
111 220 330 221 331 333 231 201
110 200 300 211 311 332 213
100 202 303 212 313 322 012
101 020 030 131 232 123 021
010

I missed some too, but that's 54
(the smarter way to do it is simply 4^3=64)
which is 8X more storage space. (800%)
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post #62 of 69
[quote]

Originally posted by MajorMatt:
Very Interesting, although the complexity grows exponentially with such an idea.

So I'd gather, the input signals are fed through some sort of voltage comparators and depending upon the gate, it makes a a voltage decision (output)

Using 0,1,2,3 look at what you get:

000 002 003 112 113 323
001 022 033 122 133 223
011 222 333 121 333 233
111 220 330 221 331 333
110 200 300 211 311 332
100 202 303 212 313 322
101 020 030 131 232
010

42 combinations over 8 combinations with just base2 (unless I made some mistakes) 80% More!
------------------------------------------------------------------------
Yeah, you missed a bunch

000 002 003 112 113 323 132 102
001 022 033 122 133 223 321 120
011 222 333 121 333 233 312 210
111 220 330 221 331 333 231 201
110 200 300 211 311 332 213
100 202 303 212 313 322 012
101 020 030 131 232 123 021
010

I missed some too, but that's 54
(the smarter way to do it is simply 4^3=64)
which is 8X more storage space. (800%)

<hr></blockquote>

Actually it is 4^4 = 256

Here is the full set:

0000 0001 0002 0003
0010 0011 0012 0013
0020 0021 0022 0023
0030 0031 0032 0033

0100 0101 0102 0103
0110 0111 0112 0113
0120 0121 0122 0123
0130 0131 0132 0133

0200 0201 0202 0203
0210 0211 0212 0213
0220 0221 0222 0223
0230 0231 0232 0233

0300 0301 0302 0303
0310 0311 0312 0313
0320 0321 0322 0323
0330 0331 0332 0333

1000 1001 1002 1003
1010 1011 1012 1013
1020 1021 1022 1023
1030 1031 1032 1033

1100 1101 1102 1103
1110 1111 1112 1113
1120 1121 1122 1123
1130 1131 1132 1133

1200 1201 1202 1203
1210 1211 1212 1213
1220 1221 1222 1223
1230 1231 1232 1233

1300 1301 1302 1303
1310 1311 1312 1313
1320 1321 1322 1323
1330 1331 1332 1333


2000 2001 2002 2003
2010 2011 2012 2013
2020 2021 2022 2023
2030 2031 2032 2033

2100 2101 2102 2103
2110 2111 2112 2113
2120 2121 2122 2123
2130 2131 2132 2133

2200 2201 2202 2203
2210 2211 2212 2213
2220 2221 2222 2223
2230 2231 2232 2233

2300 2301 2302 2303
2310 2311 2312 2313
2320 2321 2322 2323
2330 2331 2332 2333

3000 3001 3002 3003
3010 3011 3012 3013
3020 3021 3022 3023
3030 3031 3032 3033

3100 3101 3102 3103
3110 3111 3112 3113
3120 3121 3122 3123
3130 3131 3132 3133

3200 3201 3202 3203
3210 3211 3212 3213
3220 3221 3222 3223
3230 3231 3232 3233

3300 3301 3302 3303
3310 3311 3312 3313
3320 3321 3322 3323
3330 3331 3332 3333

Or more briefly,stealing from the Einsteinian tensor notation convention:

ijkl

[ 08-02-2002: Message edited by: Rick1138 ]</p>
post #63 of 69
Shit I screwed up,it is 64,I was thinking of 4 bits for some reason,anyway here is the (less) full set:

000 001 002 003
010 011 012 013
020 021 022 023
030 031 032 033

100 101 102 103
110 111 112 113
120 121 122 123
130 131 132 133

200 201 202 203
210 211 212 213
220 221 222 223
230 231 232 233

300 301 302 303
310 311 312 313
320 321 322 323
330 331 332 333
post #64 of 69
[quote]Originally posted by MajorMatt:
<strong>So I'd gather, the input signals are fed through some sort of voltage comparators and depending upon the gate, it makes a a voltage decision (output)
(...)
42 combinations over 8 combinations with just base2 (unless I made some mistakes) 80% More!</strong><hr></blockquote>

Yeah, but how do you intend to perform logical operations on four-state values? What is 3 AND 4? (Note: Saying 3 OR 4 in a four-state machine would be 0011 OR 0100 = 0111 is not an option - if you convert back to binary representation before doing the actual operation, you don't have any benefit over using a binary machine in the first place).

Bye,
RazzFazz
post #65 of 69
I have no intention of reading this entire thread, so I don't know if this has been mentioned yet, but the obvious reason why there is no base 3+ has to do with the reliability of the non-binary data.

With a limited pallette of 1 and 0, digital media gains reknowned reliability, ie cdroms, binary files, etc. The reason for this is, on a physical level, you have to screw up a 1 a WHOLE LOT before it starts looking like a 0, and vice versa. With checksums and such, even if a bit is not readable, if it is known to NOT be a 0, it therefore is a 1.

1 and 0 are electrically and physically dissimilar. As soon as you break the polar-opposite spectrum and create threes and fours, the reliability gos to shit.

1 and 0 is the way and the light.
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post #66 of 69
D'oh!

I forgot to combine them in threes, not just two's
i.e. (0:1 0:2 1:2 0:3 1:3 3:2)

And I dont know what to do or fathom about multiple voltage input gates....

PS - Does everyone know op-amps were originally intended for mathematical calculations?
post #67 of 69
Thread Starter 
[quote]Originally posted by stimuli:
<strong>I have no intention of reading this entire thread, so I don't know if this has been mentioned yet, but the obvious reason why there is no base 3+ has to do with the reliability of the non-binary data.

With a limited pallette of 1 and 0, digital media gains reknowned reliability, ie cdroms, binary files, etc. The reason for this is, on a physical level, you have to screw up a 1 a WHOLE LOT before it starts looking like a 0, and vice versa. With checksums and such, even if a bit is not readable, if it is known to NOT be a 0, it therefore is a 1.

1 and 0 are electrically and physically dissimilar. As soon as you break the polar-opposite spectrum and create threes and fours, the reliability gos to shit.

1 and 0 is the way and the light.</strong><hr></blockquote>

Yeah, several times.
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post #68 of 69

When we reach quantum computing we will be on the level of DNA. Look at it like this, a base 3 code would be like our TVs which use three colors to display a flat picture of thousands of different color variations. that could take the form of -, 0, or +. So you could have your switch go one way for - another way for 0 (no voltage) or another way for + voltage. Now that's something we already have all around us, it's called AC power. Go one more level and you would have a base 4 code like our DNA which makes us in 3D not just a flat screen. 

post #69 of 69

This WAS as 12+ year dead thread...  

 

If you added something interesting and the least bit new it might be cool.  But this way it looks like you are just prepping an accont for use as a spambot.  Your examples are rubbish by the way...

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