Re: FPGA

On Monday 13 August 2007, Jared wrote:

For example, lets see how 0.6 would be represented using only 3 digits. Based on the following table, we get the following results:

Base 2: 101 = .500 + .000 + .125 = .625
The margin of error is: .625 - .600 = .025 Error

Base 3: 121 = .333 + .222 + .037 = .592
The margin of error is: .600 - .592 = .008 Error

As you can see, base 3 is much more accurate.

You're not making a valid comparison. 3 digits of base 2 only has 8 possible combinations while 3 digits of base 3 gives 27 (237% more!). To be fair, you would need to compare 8 digits of base 2 with 5 digits of base 3, and then base 2 would have only a slight advantage of 5% more possibilities.

The trinary math system utilizes the 3 natural states of electrical current flow. A wire conducts in one direction, or the other, or not at all. Base 4 would need to have 4 states, which don’t naturally exist. A designer would need to use discrete voltage levels to make it work. This leads to noise margin problems and increased power consumption because the transistors will need to be in the active state. If the designer tried to quantize the numbers for mathematical operators, he would have to build 4 window detectors to signal when voltage represents a specific number. Just detecting the individual numbers make anything above base 3 unwieldy.

That's an efficiency and implementation problem and nothing more.

p.s. for anyone still reading. the idea that someone is WRONG is itself a binary assumption which virtually disappears when you start thinking in ternary. Instead of saying someone is WRONG, you simply say "Oh, he hasn't yet completed his journey on that subject..." And then you have a moral imperative to help him learn, instead of a moral imperative to "correct" him. Unless of course, he really is wrong, which is exceedingly rare, like one per billion or so.

This sounds exceedingly relativistic. Objective statements are either right or wrong. If someone believes a falsehood through ignorance, they may not be at fault, but the fact is they're still wrong.