binary numbers and computers

[Asghar baig]

Computer understands information only in binary format i.e. in the form of zeros and ones. Do you think that Binary number system is essential for computers to understand and process the information OR do you think that any other number system can be more powerful than Binary number system? Post your answers with valid arguments?

[r035198x]

Computer understands information only in binary format i.e. in the form of zeros and ones. Do you think that Binary number system is essential for computers to understand and process the information OR do you think that any other number system can be more powerful than Binary number system? Post your answers with valid arguments?

Unfortunately I may not be able to give a "valid argument". All I know is that a switch is either on or off.

[Banfa]

I think there have been computers that have worked in systems other than the binary system. There have been tertiary computers, i.e. base 3 (not sure what voltage levels they used for 0, 1, 2 may be -ve 0 +ve).

I can't think of any reason why they would have any advantage over binary systems which is probably why binary systems are prevailent since they are easy to design.

[r035198x]

I think there have been computers that have worked in systems other than the binary system. There have been tertiary computers, i.e. base 3 (not sure what voltage levels they used for 0, 1, 2 may be -ve 0 +ve).

I can't think of any reason why they would have any advantage over binary systems which is probably why binary systems are prevailent since they are easy to design.

Fuzzy logic?

[DeMan]

(IMHO) The easy thing with binary is that there are 2 states. Something is on, or something is off, something can't be a little bit on. That having been said, so long as we can accurately (and definitively) measure how much something is (and this could go beyond current - eg light frequency/sound frequency/amplitude) and then could generate the aforementioned to those frequencies, there is no reason why we couldn't have a computer that works on something other than binary.

The biggest problem, however (and many will deny this because the theory is that computers working in binary is one of the things that is keeping machines from ever being able to replicate intelligence - sure they can mimic <and of course it depends how you define intelligence, so we leave the philosophy out>), is that no matter how much we pretend otherwise, computers are simple(ish) to understand because they are binary. Boolean logic sort of goes out the window when you work beyond binary. Even the coping with data loss through noise (you know parity bits and things) become unfathomable, instead of trying to determine whether a bit should have been a one or a zero, you have to be able to work out whether a nit (sorry couldn't resist but if a Binary digIT is a bit then an N-ary digIT must be a NIT) is a 1 or an f or a 642. That having been said, I don't think these are necessarily insermountable problems, but at the very least they would require a MASSIVE rethink on how we do all of our computing today (not to thing of potential compatibility problems when using bases other than 2^n).

SHORT ANSWER: Binary is not essential, but given how long we've used binary for, it is comfortable, it works and alternatives aren't necessarily better.

{total aside (which I think merits a mention) why do we use a decimal system for every day life? (and yes I know not everyone has decimal everything, but humans compute decimal well, even though 60 (which we use in time) is a better option because it is divisible by the primes 2,3,5 (or even 30). Is it deliberate that round things seem to conform to 30 or 60 (clocks, degrees,....etc, etc, etc) We have been trained to use numbers a certain way and find them convenient, but time and time again nature proves the fibonacci sequence to somehow be important - yet most peiople you meet wouldn't even thin k there is anything special about 21 or 5 or 34 - I've digressed too far so I stop now}

[acoder]

Good explanation, DeMan.

I think another number system would not necessarily be more powerful. In fact, you could argue that the more simple it is, the less likelihood of bugs and problems lower down and therefore, more powerful. But I'm not too much of a hardware man, my knowledge is just limited to a bit of boolean logic and then I found the subject too boring and stuck to software and web programming.

[Predictor]

"Computer understands information only in binary format i.e. in the form of zeros and ones."

This is simply false. Though most commercially available are based on binary logic, some are not (the 8087 FPU, for instance, employed a 4-state logic). Regardless, bits can be and are composed into groups (byte, "reals", etc.), allowing representation of larger numbers of values in a single symbol.

[Banfa]

Actually there are also 3 state computers I believe.

However at a fundamental level in pure mathematics there are only 2 significant numbers, 0 and 1. All other numbers are just a way of representing those numbers in a form convenient for the current use.

A binary (2 state logic) computer by definition deals with 2 states, 0 and 1. In something like a byte all you have done is collect a group of states together, the computer itself has no concept of that group of bits representing some larger concept such as an 8 bit number or a floating point number. It operates on the 0s and 1s according to a set of (relatively) simple rules to produce more 0s and 1s. Those bits might be used to draw a pattern on the display unit but it is your brain that interprets that pattern as a digit with a larger value (5 for example). The (binary) computer only knows about 0 and 1.

[Predictor]

"However at a fundamental level in pure mathematics there are only 2 significant numbers, 0 and 1."

The only thing "fundamental" about a 2-state variable is that it involves the smallest whole number of distinct states possible while still permitting variation. Information theory applies to 3-state variables, 5-state variables and 114-state variables, exactly as it does to 2-state variables. In fact, Shannon wrote about exactly this when he developed information theory back in 1948. See "The Mathematical Theory of Communication", by Claude Shannon.

"All other numbers are just a way of representing those numbers in a form convenient for the current use."

I would say rather that they are (or can be) equivalent. There is no meaningful sense in which we would say that "4-state variables are really 2-state variables in disguise".

"A binary (2 state logic) computer by definition deals with 2 states, 0 and 1. In something like a byte all you have done is collect a group of states together, the computer itself has no concept of that group of bits representing some larger concept such as an 8 bit number or a floating point number. It operates on the 0s and 1s according to a set of (relatively) simple rules to produce more 0s and 1s. Those bits might be used to draw a pattern on the display unit but it is your brain that interprets that pattern as a digit with a larger value (5 for example). The (binary) computer only knows about 0 and 1."

I suppose that this is a matter of abstraction. Consider 256-state variables, which may be represented as 8-bit bytes. Operations may be carried out on these 256-state values as though they were 256-state values (such as addition). Such operations may be mimicked using groups of binary operations on collections of 8 bits, but that does not mean that these operations are somehow "really" binary. It means that they are equivalent.


-Will Dwinnell