Transistors are generally at their lowest static power dissipation if the are either fully on or off. The analog middle is great if you're trying to process continuous values, but then you're going to be forced to use a bias current to hold on in the middle, which is ok if that's the nature of the circuit.
A chip with billions of transistors can't reasonably work if most of them are in the analog mode, it'll just melt to slag, unless you have an amazing cooling system.
Also consider that there is only one threshold between values on a binary system. With a trinary system you would likely have to double the power supply voltage, and thus quadruple the power required just to maintain noise margins.
This is great point, and I'll extend it by claiming that there's a more general physical principle underneath: that it's significantly easier to build bistable systems than tristable (or higher) systems, so much so that it makes up for the fact that you need more of them.
This is far more general than electronic systems (e.g. quantum computers follow the same principle - it's far easier to build and control qubits than qutrits/qudits).
(technically, it's even easier to build systems that have a single stable configuration, but you can't really store information in those, so they're not relevant)
It can be solved various ways, not only middle, electricity has negative voltages too. So you can have the third distinct "fully on" state at negative voltage. This isn't practical with silicon semiconductors but might be possible with other technology. The Soviet ternary computer Setun used custom ternary switches.
there is nothing special about negative voltages, it's all relative to some point anyway.
With mixed analog/digital circuits for example, it's pretty common to treat exactly same voltages either as -2.5/0/2.5 (relative to midpoint), or as 0/2.5/5 (relative to negative rail).
What matters is having multiple treshold voltages with distinct behaviour. Setun used ferrite transformers which do have multiple thresholds (postive and negative fields) - but modern electronics, including transistors, does not.
Wouldn't you also get data loss using the linear region of transistors? The output would be have some error from the input and it would propagate through the circuit, perhaps eventually reaching on or off where it would be stuck.
Trinary is an efficient way of storing lots of -1/0/1 machine learning model weights. But as soon as you load it into memory, you need RAM that can store the same thing (or you're effectively losing the benefits: storage is cheap). So now you need trinary RAM, which as it turns out, isn't great for doing normal general purpose computation with. Integers and floats and boolean values don't get stored efficiently in trinary unless you toss out power of two sized values. CPU circuitry becomes more complicated to add/subtract/multiply those values. Bitwise operators in trinary become essentially impossible for the average IQ engineer to reason about. We need all new IAs, assembly languages, compilers, languages that can run efficiently without the operations that trinary machines can't perform well, etc.
So do we have special memory and CPU instructions for trinary data that lives in a special trinary address space, separate from traditional data that lives in binary address space? No, the juice isn't worth the squeeze. There's no compelling evidence this would make anything better overall: faster, smaller, more energy efficient. Every improvement that trinary potentially offers results in having to throw babies out with the bathwater. It's fun to think about I guess, but I'd bet real money that in 50 years we're still having the same conversation about trinary.
I once tried to start enumerating gate types for Trinary.
In binary, with two inputs, there are 2^2 = 4 total possible inputs (00, 01, 10, 11). Different gate types can give different outputs for each of those four inputs: each output can be 0 or 1, so that's 2^4 == 16 different possible gate types. (0, 1, A, B, not A, not B, AND, OR, NAND, NOR, XOR, XNOR, A and not B, B and not A, A or not B, B or not A)
In ternary, with two inputs, there are 3^2 = 9 total possible inputs, so 3^9 = 19,683. I'm sure there are some really sensible ones in there, but damn that's a huge search space. That's where I gave up that time around! :-)
> Trinary didn’t make any headway in the 20th century; binary’s direct mapping to the “on”/”off” states of electric current was just too effective, or seductive; but remember that electric current isn’t actually “on” or “off”. It has taken a ton of engineering to “simulate” those abstract states in real, physical circuits, especially as they have gotten smaller and smaller.
But, I think things are actually trending the other way, right? You just slam the voltage to “on” or “off” nowadays—as things get smaller, voltages get lower, and clock times get faster, it gets harder to resolve the tiny voltage differences.
Maybe you can slam to -1. OTOH, just using 2 bits instead of one... trit(?) seems easier.
Same reason the “close window” button is in the corner. Hitting a particular spot requires precision in 1 or 2 dimensions. Smacking into the boundary is easy.
The lower voltage helps reduce leakage and capacitance in the chip as the wires get closer together.
But it does argue against more states due to the benefits of just making 1 smaller if you can and packing things closer. Though maybe we are hitting the bottom with Dennard scaling being dead. Maybe we increase pitch and double state on parts of the chip, and then generations are measured by bits per angstrom.
Not quite. Leakage current in CMOS circuits became the dominant source of power consumption around the 90 nm and 65 nm nodes, long before quantum tunneling was a major factor, and often exceeded dynamic switching power. This led to the introduction of multiple threshold-voltage devices and body-biasing techniques to dynamically adjust Vt and curb static leakage.
There's a ton of places in modern silicon where a voltage represents far more than just on or off. From the 16 levels of QLC to the various PAM technologies used by modern interconnects
And the first thing you do to them is to convert them to binary.
Look at any Ethernet PHY for example - you have that nice 5-level signal coming on.. and the first thing you do is feed it into AFE/ADC so you get digital signals that you can actually work with.
So yes, in some specific situations, like Flash memory or interconnects, there are multi-level signals. But the computing itself is always binary.
I’ve wondered any number of times if 4 level gates would be useful to increase cache memory in CPUs. They aren’t great for logic, but how much decoding would they need to expand an L3 cache?
> Trinary is philosophically appealing because its ground-floor vocabulary isn’t “yes” and “no”, but rather: “yes”, “no”, and “maybe”. It’s probably a bit much to imagine that this architectural difference could cascade up through the layers of abstraction and tend to produce software with subtler, richer values … yet I do imagine it.
You can just have a struct { case yes; case no; case maybe; } data structure and pepper it throughout your code wherever you think it’d lead to subtler, richer software… sure, it’s not “at the hardware level” (whatever that means given today’s hardware abstractions) but that should let you demonstrate whatever proof of utility you want to demonstrate.
Most usages of a 'bool' are taking up at least a byte, so everyone has 250-odd extra values to play with "at the hardware level" already if they really want.
This - we don't directly bit-address much in computing, so the idea that richness isn't there because of binary is kind of silly. The flexibility is there and you often pay for it either way.
On many 64-bit architectures, you actually waste 63 bits of extra padding for that boolean, for alignment reasons, unless you put some other useful data nearby in your struct (according to the alignment rules).
Luckily, this kind of waste doesn't happen often, but sadly, it does sometimes happen.
I've never understood the fascination here. Apparently some expression relating the number of possible symbols and the length of a message is closer to euler's number. I don't see why the product of those things is worth optimizing for. The alphabet size that works best is dictated by the storage technology, more symbols usually means it's harder to disambiguate.
2 is the smallest amount of symbols needed to encode information, and makes it the easiest to disambiguate symbols in any implementation, good enough for me.
The idea is roughly that the effort needed to use a system is in some situations ~propto the number of symbols * the number of needed positions.
Here's a concrete example, imagine you needed to create some movable type because you are creating a printing press. And you need to represent all numbers upto 100 million.
In binary you need to make 53 pieces, in ternary 50, in octal 69 pieces, in decimal 81 and in hexadecimal 101.
> In binary you need to make 53 pieces, in ternary 50, in octal 69 pieces, in decimal 81 and in hexadecimal 101.
These numbers don't quite make sense to me. Hexadecimal should have 16 symbols, and then `log16(whatever) = message length`. I get what you're trying to say though.
That trend continues up until the symbols start looking the same and no one can read them, and now the most important problem is not a position on a tradeoff curve. It's that the system is no longer reliable.
If you wanted each letter to have the highest probability of successfully being read, you would use a grid, and shade or leave blank each grid square.
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A chip with billions of transistors can't reasonably work if most of them are in the analog mode, it'll just melt to slag, unless you have an amazing cooling system.
Also consider that there is only one threshold between values on a binary system. With a trinary system you would likely have to double the power supply voltage, and thus quadruple the power required just to maintain noise margins.
This is far more general than electronic systems (e.g. quantum computers follow the same principle - it's far easier to build and control qubits than qutrits/qudits).
(technically, it's even easier to build systems that have a single stable configuration, but you can't really store information in those, so they're not relevant)
With mixed analog/digital circuits for example, it's pretty common to treat exactly same voltages either as -2.5/0/2.5 (relative to midpoint), or as 0/2.5/5 (relative to negative rail).
What matters is having multiple treshold voltages with distinct behaviour. Setun used ferrite transformers which do have multiple thresholds (postive and negative fields) - but modern electronics, including transistors, does not.
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So do we have special memory and CPU instructions for trinary data that lives in a special trinary address space, separate from traditional data that lives in binary address space? No, the juice isn't worth the squeeze. There's no compelling evidence this would make anything better overall: faster, smaller, more energy efficient. Every improvement that trinary potentially offers results in having to throw babies out with the bathwater. It's fun to think about I guess, but I'd bet real money that in 50 years we're still having the same conversation about trinary.
In binary, with two inputs, there are 2^2 = 4 total possible inputs (00, 01, 10, 11). Different gate types can give different outputs for each of those four inputs: each output can be 0 or 1, so that's 2^4 == 16 different possible gate types. (0, 1, A, B, not A, not B, AND, OR, NAND, NOR, XOR, XNOR, A and not B, B and not A, A or not B, B or not A)
In ternary, with two inputs, there are 3^2 = 9 total possible inputs, so 3^9 = 19,683. I'm sure there are some really sensible ones in there, but damn that's a huge search space. That's where I gave up that time around! :-)
But, I think things are actually trending the other way, right? You just slam the voltage to “on” or “off” nowadays—as things get smaller, voltages get lower, and clock times get faster, it gets harder to resolve the tiny voltage differences.
Maybe you can slam to -1. OTOH, just using 2 bits instead of one... trit(?) seems easier.
Same reason the “close window” button is in the corner. Hitting a particular spot requires precision in 1 or 2 dimensions. Smacking into the boundary is easy.
But it does argue against more states due to the benefits of just making 1 smaller if you can and packing things closer. Though maybe we are hitting the bottom with Dennard scaling being dead. Maybe we increase pitch and double state on parts of the chip, and then generations are measured by bits per angstrom.
Well, until we scaled transistors down to the point where electrons quantum tunnel across the junction. Now they're leaky again.
Look at any Ethernet PHY for example - you have that nice 5-level signal coming on.. and the first thing you do is feed it into AFE/ADC so you get digital signals that you can actually work with.
So yes, in some specific situations, like Flash memory or interconnects, there are multi-level signals. But the computing itself is always binary.
You can just have a struct { case yes; case no; case maybe; } data structure and pepper it throughout your code wherever you think it’d lead to subtler, richer software… sure, it’s not “at the hardware level” (whatever that means given today’s hardware abstractions) but that should let you demonstrate whatever proof of utility you want to demonstrate.
On many 64-bit architectures, you actually waste 63 bits of extra padding for that boolean, for alignment reasons, unless you put some other useful data nearby in your struct (according to the alignment rules).
Luckily, this kind of waste doesn't happen often, but sadly, it does sometimes happen.
2 is the smallest amount of symbols needed to encode information, and makes it the easiest to disambiguate symbols in any implementation, good enough for me.
Here's a concrete example, imagine you needed to create some movable type because you are creating a printing press. And you need to represent all numbers upto 100 million.
In binary you need to make 53 pieces, in ternary 50, in octal 69 pieces, in decimal 81 and in hexadecimal 101.
These numbers don't quite make sense to me. Hexadecimal should have 16 symbols, and then `log16(whatever) = message length`. I get what you're trying to say though.
That trend continues up until the symbols start looking the same and no one can read them, and now the most important problem is not a position on a tradeoff curve. It's that the system is no longer reliable.
If you wanted each letter to have the highest probability of successfully being read, you would use a grid, and shade or leave blank each grid square.