Binary-base 2 electronics. Theoretically What if computers, and electronics, operated on b10, or b26??

Question

I understand how binary works, and for the most part, how circuit boards work. I'm just wondering, on part as research for a book I'm working on, but overall, wondering in some small way, if electronics companies are doing too much research in the wrong directions. Ex., dual core processors, that's not overly a huge breakthrough, and looking at the way a computer processor works, it's got to reach a ceiling sometime. I mean, 1GHz, how many times a second is that.... Anyway, the big question(s) would be if the speed and power would increase exponentially, or or if it would be impossible to even guess what changing base 2 to b4 would result in. I obviously can't give an example, but any answers would be appreciated!

Answer 1

Some early computers used base 10. But any base can be represented in base 2 ans on/off is an easy concept to construct in hardware.

I have often thought about the advantages of a three-state (base 3) system (which would also be fairly easy to construct in hardware using +, 0, and - voltages) that would allow the representation of neurological functions - excitatory, neutral, or inhibitory. But, like all other bases, base 3 can be represented in binary, so I'm not sure that the advantages outweigh the difficulties.

Answer 2

ALL electronic circuitry comes down to ON vs OFF and Binary digits of 0 and 1 can represent this.     The transistor is the basis for building microprocessors and is based on the "on / off" concept.

Answer 3

I know that binary is the easiest for a computer to work with, because it can give a simple yes/no type coding for a computer. If base 4 were used, there is a grey area that a computer will not recognise properly. It can be yes, no, or some "maybe" answers, and "maybe" is a term humans can understand, but computers can't.

For the rest, I don't know.

Answer 4

I agree that base 3 should be better than base 2, but looking at actual circuitry for adders, flip flops, and memory cells, they use more than the additional digit buys you. In addition, base 2 has only two threshholds, one for low and one for high. For base 3, there are 4: two around zero. The circuitry is too costly. Thus, base 2 is most efficient.

Other bases would be far more expensive to implement directly in hardware. Representing an arbitrary base like b26 would be prohibitively expensive, essentially trying to use analog representation of a digital value. Computers are already in base 2, and thus automatically are also in multiples: base 4, base 8, base 16, base 32, base 64. Using any of these require  no hardward changes, and only minor software changes in compilers and such to use the alternate bases.

In fact, most general purpose computers do base 10 arithmetic; this is done by using base 16 circuitry in the Arithmatic Logic Unit (4 binary digits per base 10 digit), and adjusting carry flags and such for base 10, sometimes refered to as BCD or binary coded decimal.

So, answer is, they would still do them in a multiple base of base 2. In the case of b26 they would probably use base 32, and adjust down because it is much easier and cheaper than to use more than 2 voltage levels. Using b32 would require some additional circuitry, because most hardware is oriented toward multiples of 4 bit slices.

By the way, I think the electronics companies have by and large been excellent at directing their R&D to develop electronics. There is little doubt computers will be hundreds of times faster in only a few years. Dual processors are pretty much a waste, but are precursors to multi-processor machines as operating system software improves. I've seen quad core stuff already, and massively parrallel processing probably is not that far away. And, Gigaherz is 1 billion times per second.

Answer 5

What your asking is why we don't have analog computers...

Edit:  Dealing with BCD and other Base Values is still done in binary. BCD is "Binary" Coded Decimal .  Advantages to BCD allows easy grouping of ASCII data in a form that is easier to display. The disadvantage is that BCD takes more memory to represent a number.   255 takes 8 bits to rpresent in binary but would require a minimum of 12 bits  in BCD.

BCD math operations are less efficient as additional carries are necessary for each digit rather than single carries for a binary word

Binary is represented by two states On or Off for each digit.  Or the presence  (binary 1) or absence (binary 0) of a voltage (or voltage level necessary to operate an electronic switch)

Base2 Binary each digit is represented by two states On or Off (a.k.a.  High or Low).   Base10 values are represented by conversion in to multiple digits of binary (Base2)  

9decimal = 00001001 in binary

To represent  more than two states per digit, such as base 10 would require the representation and detection of multiple voltage levels per digit.  (10 levels for base 10)   . By doing this you no longer have a yes/no situation that can be simply implimented, instead you have to measure and determine the specific voltage level.  So a 5VDC voltage would be broken down into 10 distinct voltage levels of .5vdc steps to represent the numbers 0 to 9.   (This in an analog representation of base 10)

The circuitry to perform such analog measurments is much more complex than a base2 digital equivalent.  There are also issues with the accuracy of analog systems and the potential for error.     In the above example  a 0.25 volt level could easily be determined to be a zero (base10)  what if that same signal was 0.499 VDC ?  It is still a zero but will the analog circuit be accurate enough to determine  it is a zero and NOT call it a one. This is the problem with analog computer is the potential to inject measurement errors into the numeric data.

As for upper limits of speed consider that electrons travel at light speed the distance an electron can travel.  In one nano second an electron can travel 11.75 inches.   1nsec is the wave lenght for 1Ghz. (1000000000 hz)  so at 2.4Ghz an electron travels just under 5 inches.   Since electrons need to travel from register to register in a CPU there will be an end point in frequency by which the process cannot not go any faster because electrons won't have time to travel necessary distances. Like to and from memory not just within the CPU.    Considering the die sizes of a cpu I would say that we have a ways to go before hitting that theoretical wall for CPU processes.  Certainly distances to other chips such as memory will be a factor long before hitting the CPU limit.   For a 10GHz Cpu (electron travels 1 inch per cycle) the CPU would have to wait several cycles for data to arrive from a memory chip that is several inches away.

Parallel processing and memory integrated with the CPU would be ways to deal with the speed distance issue

Answer 6

binary is the most efficient base for computers, anything else would slow them down, as they would have to convert to binary each number before doing any calculations.