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I like the ancient Babylonian method of counting on one's fingers. Forgetting the thumb, there are 3 segments to each finger. That means you can count to twelve on 1 hand. When you reach 12 you mark 1 on your other hand. Starting with the tip of the left index finger you check all 3 segments on that finger, then move to the middle finger & so on.Thumbs were used to touch the relevant finger segments so touching the 2nd segment of the middle finger, left hand and 3rd segment index finger of the right hand you are indicating 3*12+5=41. The max number you can count to is 144 (assuming you have 4 fingers on each hand).12 is a more efficient base than 10 as 12 is divisible by 2, 3, 4 & 6. 10 is only divisible by 2 & 5. Common fractions are readliy calculable in base 12 too. You have use decimal places for any fractions other than 1/2 or 1/5. Base 12 allows 1/4, 3/4, 2/3 etc. I sometimes wish the Babylonian system had come to the fore rather than the base 10 system we now use.
I think you have to look at the two hands as, effectively, ten different symbols in a decimal system. In which case, you would need about three such symbols to transmit 10E3 different states which is roughly the same number of states that can be sent with ten binary digits. (This is a fairly common computer thing - as in kB often meaning 1024Bytes.)I must say, I hadn't imagined, in my remotest dreams that "raised finger" could be taken in that way but, on re-reading, I see that it could have been.
Make it Lady, I did give a sensible, and I believe mathematically correct, answer but it was obviously considered too boring to bother with.
You'd need three-state logic for trinary, four-state logic to work in base four etc.
Actually three states is more efficient as a number system, but two states is easier to implement in logic because logic is based on something being true or false - a natural two state system.
Umm... "a trinary J-K flip-flop..."Do you want to think that one through again? You can't really use several bits i.e. two bits to work in trinary because it's not just a question of how you store the data but also how you operate on that data. Even though you could use two bits to represent trinary or base four, the underlying operations will still be binary because the logic is still two-state. In trinary you need to not only work with tits, rather than bits, but also with three-state logic, hence my comment re a trinary flip-flop. For example, if we use -1, 0 & +1 for our trinary states, what would be the opposite of each state?
Jason Fong asked the Naked Scientists: Hi Chris,As we all know the standard qwerty keyboard layout is rather inefficient, error prone and slow. After all in school we learn that it was designed to slow down "typewritists". After stumbling into the dvorak keyboard layout whilst trying to increase my characters per minute typed, I suddenly began to question the efficiency of codes such as binary. Is binary inherently the most efficient way of representing any set data using two states? Or is it just efficient in conveying a set number of characters? Or should I be asking about the efficiency code which is written in binary?Also would the complexity of computer code increase linearly or exponentially as we hopefully in the future mature into quantum computing? Perhaps binary is only efficient for linear calculations, I read that quantum computing will allow multi threaded algorithms, such as the ones used to calculate large primes, to run much faster/efficiently.What do you think?
Ternary can be used in computing though we are not really used to thinking in this way. I have a suspician that it would have been quite hard to think of the design of a multi-bit adder in binary for the first time (a cascade of full adders with carry) and 2's complement arithmatic is not all that obvious. The problem with ternary is that detecting 2 states (high or low) is easy in electronics but a third state would demand some sort of window comparator or, alternatively, running 2 lines from every output. So basically binary is well suited to mapping on to the hardware and efficient in terms of silicon real estate.
Modern types of writable RAM generally store a bit of data in either the state of a flip-flop, as in SRAM (static RAM), or as a charge in a capacitor (or transistor gate), as in DRAM (dynamic RAM), EPROM, EEPROM and Flash.
I was wondering about how this could be implemented in 'silicon' (but I fear I may only know enough to make a fool of myself here).The wikipedia article on Computer Memory (Random-access memory):http://en.wikipedia.org/wiki/Random-access_memorysays...QuoteModern types of writable RAM generally store a bit of data in either the state of a flip-flop, as in SRAM (static RAM), or as a charge in a capacitor (or transistor gate), as in DRAM (dynamic RAM), EPROM, EEPROM and Flash.Hmm... I'm not sure about how using charge in a capacitor is implemented in practice, but both the flip-flop SRAM and transistor gate DRAM methods are both inherently binary devices. A tri-state flip-flop, as discussed earlier, seems to be a bit of a contradiction in terms, and I think we might need a sort of combined pnp/npn transistor to use the gate method. It would seem then, that the individual low-level hardware elements that would be needed to implement a trinary hardware system would be more complex, as graham.d says.Heh, while the idea of trinary seems relatively straightforward, at first glance, actually implementing it might be a lot trickier that you'd expect. It makes me wonder how significant it is that no one appears to have made a trinary computer system since that 1950's Russian one; if it were easy, then I think it would have happened but as it hasn't, then it probably isn't.
Geezer and Lee, actually modern Flash memories already use multiple levels (see MLC Flash). Of course it is hard to get a high yield so there is a huge amount of error correction used but it saves a lot of chip area. It has been tried in Dynamic memories too but without much commercial success. It is hard to see how to use it in SRAM (more or less by definition). The multiple levels tend to be binary related (4, 8, 16), but this is because of the logic following will be binary. There is nothing to prevent 3 or 9 states being used.