Why Computers Use Binary

Binary numbers – seen as strings of 0's and 1's – are often associated with computers. But why is this? Why can't computers just use base 10 instead of converting to and from binary? Isn't it more efficient to use a higher base, since binary (base 2) representation uses up more "spaces"?

I was recently asked this question by someone who knows a good deal about computers. But this question is also often asked by people who aren't so tech-savvy. Either way, the answer is quite simple.

What is "digital"?

A modern-day "digital" computer, as opposed to an older "analog" computer, operates on the principle of two possible states of something – "on" and "off". This directly corresponds to there either being an electrical current present, or said electrical current being absent. The "on" state is assigned the value "1", while the "off" state is assigned the value "0".

The term "binary" implies "two". Thus, the binary number system is a system of numbers based on two possible digits – 0 and 1. This is where the strings of binary digits come in. Each binary digit, or "bit", is a single 0 or 1, which directly corresponds to a single "switch" in a circuit. Add enough of these "switches" together, and you can represent more numbers. So instead of 1 digit, you end up with 8 to make a byte. (A byte, the basic unit of storage, is simply defined as 8 bits; the well-known kilobytes, megabytes, and gigabytes are derived from the byte, and each is 1,024 times as big as the other. There is a 1024-fold difference as opposed to a 1000-fold difference because 1024 is a power of 2 but 1000 is not.)

Does binary use more storage than decimal?

On first glance, it seems like the binary representation of a number `10010110` uses up more space than its decimal (base 10) representation `150`. After all, the first is 8 digits long and the second is 3 digits long. However, this is an invalid argument in the context of displaying numbers on screen, since they're all stored in binary regardless! The only reason that `150` is "smaller" than `10010110` is because of the way we write it on the screen (or on paper).

Increasing the base will decrease the number of digits required to represent any given number, but taking directly from the previous point, it is impossible to create a digital circuit that operates in any base other than 2, since there is no state between "on" and "off" (unless you get into quantum computers... more on this later).

What about octal and hex?

Octal (base 8) and hexadecimal (base 16) are simply a "shortcut" for representing binary numbers, as both of these bases are powers of 2. 3 octal digits = 2 hex digits = 8 binary digits = 1 byte. It's easier for the human programmer to represent a 32-bit integer, often used for 32-bit color values, as `FF00EE99` instead of `11111111000000001110111010011001`. Read the Bitwise Operators article for a more in-depth discussion of this.

Non-binary computers

Imagine a computer based on base-10 numbers. Then, each "switch" would have 10 possible states. These can be represented by the digits (known as "bans" or "dits", meaning "decimal digits") 0 through 9. In this system, numbers would be represented in base 10. This is not possible with regular electronic components of today, but it is theoretically possible on a quantum level.

Is this system more efficient? Assuming the "switches" of a standard binary computer take up the same amount of physical space (nanometers) as these base-10 switches, the base-10 computer would be able to fit considerably more processing power into the same physical space. So although the question of binary being "inefficient" does have some validity in theory, but not in practical use today.

Why do all modern-day computers use binary then?

Simple answer: Computers weren't initially designed to use binary... rather, binary was determined to be the most practical system to use with the computers we did design.

Full answer: We only use binary because we currently do not have the technology to create "switches" that can reliably hold more than two possible states. (Quantum computers aren't exactly on sale at the moment.) The binary system was chosen only because it is quite easy to distinguish the presence of an electric current from an absense of electric current, especially when working with trillions of such connections. And using any other number base in this system ridiculous, because the system would need to constantly convert between them. That's all there is to it.

Saturday, May 15, 2010 at 9:47 PM
Read it all, and excellant post, Lyosha!

Yeah, I do wonder how future computers will be.

Like you said, in binary, you have two modes, on/off, so it does make sense to be in a computer.

Who would even use a quantum computer?
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Monday, May 17, 2010 at 12:27 AM
@Taylor Jasko Quantum computers are a thing of the future. Who will use them? Everybody, much like people use regular transistor-based computers and devices today. Why quantum? Because they solve the many inevitable problems of today's transistor-based computers, such as the physical universe's limitations of transistor density (Moore's Law won't last forever).
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Ben
Wednesday, October 6, 2010 at 6:08 PM
@nookkin Technicaly a "quantum computer" is possible by simply varying the current or making a different path for the current to travel, or a combination of both.
On the topic of moores law,
if you go by definition then moore's law isn't realy a law, it is just an uncannily accurate observation and prediction. Why they called it moore's law when it should be called Moore's Theory of computer miniatureization
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Sujit
Friday, December 24, 2010 at 3:33 PM
Whats a nice description, really mind blowing
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Ben
Saturday, December 25, 2010 at 9:56 AM
Thanks, sujit.
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jayvin
Sunday, January 23, 2011 at 2:43 PM
These "on/off" states (at least as far as signal transmission goes anyway) could be changed from (0volts/5volts) to (0volts/1volt/2volts/3volts/4volts...) so you could get a base 16 if you wanted (or base 10 for ease of human understanding), but I am not familiar with how the "switches" work, so storing this data might be harder (as stated in original article). but investigation into this area (of creating multi-state switches) will probably be a valuable research field in the near future.
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Jayxx1234
Sunday, January 23, 2011 at 2:45 PM
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Sunday, January 23, 2011 at 3:47 PM
@jayvin That's definitely possible, but it would involve far more complicated circuitry and might simply be less reliable. One of the cool things about binary is that you get a nice amount of tolerance -- "0V off, +5V on" actually has a tolerance of "0-0.5V off, +2V-+5V on", so a voltage dip won't cause too many issues. In a 6-state system (0V, 1V, 2V, 3V, 4V, 5V) for instance, a simple voltage dip or spike (i.e. static electricity, bad power supply) could corrupt data very easily.
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jayvin
Sunday, January 23, 2011 at 3:58 PM
@nookkin Good point. In that case, state1: 0-2v, state2: 3-4v, state3: 5-6v, state4: 7-8v and so on might work, or even a larger gap to allow higher tolerance? However, it would mean that components would need to handle up to say 20v without burning out or damaging. This might be too much worry for too little gain, but its a theory anyway.
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Ben
Monday, January 24, 2011 at 8:24 PM
@nookkin Well, you wouldn't exactly want a super expensive, super sensitive quantum computer to be open to static electricity and plugged into a wall socket, they would have them In a lab plugged into their own power generator that is checked and maintained every 10 minutes just for the reasons that you mentioned and also so that they could use smaller, more precise amounts of varying currents.
Also, no one has mentioned the different paths idea.
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Wednesday, January 26, 2011 at 10:56 AM
@Ben That definitely makes sense, but it means that this technology won't be seen by end users until they alleviate those issues. Unless they alter the way memory is stored, i.e. it's currently stored using "on" and "off" cells but could theoretically be stored via one of many orientations of electrons, it won't have much of a practical use.

The "different paths" idea still reduces to 2 discrete voltage states, making it expressible using binary. (Please correct me if I'm wrong here.)

Those are pretty cool ideas though, and I guess I'll be dealing with huge paradigm shifts in computers as I get older and the limits of current computers are reached.
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Ben
Friday, January 28, 2011 at 6:27 PM
Well, computers do already use something else to store info, namely very shallow groves in the surface of the CDs and DVDs and the spacing, depths, and lengths of these groves indicate the data. These are very efficient ways to store data and allow a near limitless amount of possibilities of data.

The quantum computers would be used in labs for a long while they refine them to handle end users and, eventually, small enough for a home desktop.
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Saturday, March 19, 2011 at 2:43 AM
Thank you so much for this simple explanation. I have to imagine that multi-state switches are what will allow our computing power to continue to increase exponentially.
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Cypher
Thursday, June 16, 2011 at 9:26 PM
@Taylor Jasko I would
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azyr
Tuesday, July 12, 2011 at 10:38 PM
i do really love numbers !!!
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Thursday, July 28, 2011 at 4:58 PM
I'm not a computer guy, but I'm taking a Computer Technology class for my teaching credential, and we went over a simulation of the calculations of a binary system and compared it to a decimal system. Since the decimal system counted in terms of 1/100 it took a hugely greater amount of time than the binary system. It seemed like binary was faster, but base 10 would be more powerful. Am I understanding this correctly?
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Thursday, July 28, 2011 at 6:20 PM
@Chuck They're both equally "powerful" in that they store numbers.

Binary is far more efficient for today's computers to process because it's easy to build a reliable circuit that has distinct "on" and "off" states. Two values in the real world imply the use of a 2-valued number system.

Binary is also simpler; the basic operations of addition and subtraction only involve 3 possible states (0, 1, carry/borrow) versus 11 possible states for decimal.

Decimal is significantly more intuitive for humans, however, since a) we normally have 10 fingers and b) our language was built around a base-10 system.
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Izzy
Thursday, September 1, 2011 at 6:32 PM
ik u can only have on or off but instead of that, y not use something else? such as light? and something in between the sender and receiver to bend light? so u can have inf amount of... therefore u can represent anything w/ lights. so like this:
S 0 R
s=sender r=receiver 0 glass or some shit.
0 will be kinda like glasses but movable by the computer to make any character.
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Saturday, September 3, 2011 at 7:28 PM
@Izzy Sending light through glass fibers is quite commonly in use today -- it's known as "fiber optics." (They use it for internet connections, optical S/PDIF audio, and more.)

There are still limits as to how much information you can send -- namely, the speed of light, and the attenuation caused by a non-100%-clear cable over longer distances. It's still significantly faster than copper wire and has the additional benefit of not being influenced by EM interference or varying ground potential (over long distances).

Light is still used digitally though, through on/off pulses. It's easy to send tons of fast, timed on/off pulses, but it's much more difficult and error-prone to measure analog levels of light. You need something that has well-defined quantum states, and unless we're talking positions of an electron or something like that, the only ones that can be easily achieved are "off" and "on."
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subhashh thakur
Wednesday, September 21, 2011 at 3:42 AM
mie compter ca techer laugh on me whn i askd him dat;

y we use binary no. in computer;

gud job be thx a lot;
pls tell me the advantages of qunatum computer over classical computers ;

iH9ns
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subhashh thakur
Wednesday, September 21, 2011 at 3:43 AM
mie compter ca techer laugh on me whn i askd him dat;

y we use binary no. in computer;

gud job be thx a lot;
pls tell me the advantages of qunatum computer over classical computers ;

iH9ns
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Wednesday, September 28, 2011 at 11:36 PM
@subhashh thakur Quantum computers greatly simplify certain mathematical calculations due to having multiple simultaneous states -- that is their main advantage.
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Coolstuff101
Tuesday, October 18, 2011 at 12:26 PM
Thank you. My teacher has confused me but thanks to your article I get it now!
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musiimenta mak bit
Friday, October 21, 2011 at 3:08 AM
people do not really love the use of numbers and that is why binary becomes the best.
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shalti singh
Wednesday, December 7, 2011 at 9:36 AM
nice answer bu ddy
i really apprecoat with the blog
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shalti singh
Wednesday, December 7, 2011 at 9:38 AM
nice answer bu ddy
i really apprecoat with the blog
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Daylon
Saturday, December 17, 2011 at 12:51 AM
Wouldnt that then be an analog circuit?
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Saturday, December 17, 2011 at 1:06 AM
@Daylon Digital circuits have very specific quantifiable states -- analog circuits are continuous and cannot be fully quantified, only approximated.
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Friday, December 30, 2011 at 10:19 AM
Would it be possible to have multiple binary circuits to make a base 10 system? For example when circuit 1 is on it represents 1 when 2 on it represents 2 etc? Or would there be complications in timing?

Oh and if higher numbers mean faster processing speeds, would a base 3 system be faster than binary? And then technology could improve from there, base 4, 5, 6.
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Friday, December 30, 2011 at 6:53 PM
@nomacromadumafropidocilicious Such a system would still be considered binary, because each circuit will have a distinct "on" and "off" state.

If you're talking about using 10 different wires for each signal (1 wire on = 1, 2 wires on = 2), it would simply be inefficient. Would you rather have 10 possible combinations or 2^10 = 1024 possible combinations for a given hardware cost?

Higher numbers do not necessarily mean faster processing speeds. It greatly depends on how the rest of the system is set up. Think about it this way: are 5 light bulbs brighter than 1? Not if there are five nightlight bulbs versus 1 100W bulb!
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Sunday, January 8, 2012 at 4:29 AM
please help me to understand better. why do computer uses binary number representation
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Ben
Monday, January 9, 2012 at 6:43 PM
Computers use binary numbers because they are SUPER simple for the computer to transcribe. Think of it like different languages. Chinese has a character for almost everything, but the English language only has 26 characters. The computer uses 2 characters. True that the "Words" have to be longer, but its easier to "remember" 2 characters as opposed to 26 characters in English or who knows how many characters in Chinese. Its also simpler to interpret those characters, because binary is actually 2 states of the computer. "On" or "off". the computer KNOWS that there is either electricity flowing through a component, or there is not. and that is much simpler than having to measure the amount of voltage in a component.
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a name
Monday, January 23, 2012 at 12:10 AM
Pretty sure base-10 computers used to exist a long time ago; they weren't produced for very long though.
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a name
Monday, January 23, 2012 at 12:31 AM
@a name "In the early 1950s most computers were built for specific numerical processing tasks, and many machines used decimal numbers as their basic number system Ă˘â‚¬â€ś that is, the mathematical functions of the machines worked in base-10 instead of base-2 as is common today. These were not merely binary coded decimal. Most machines actually had ten vacuum tubes per digit in each register."

https://en.wikipedia.org/wiki/History_of_processors#1950s:_early_designs
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kenoly
Friday, January 27, 2012 at 12:57 PM
I love this. It answers all my questions on the binary system and computer app. Im a student of computer science and i hope to ask u more questions where im confused and also hope to meet you someday.
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Mark
Tuesday, August 21, 2012 at 9:28 AM
Hi,I would like to make a point in favour of Decimal base 10 . While binary system its very simple and has today a more practical use ,( because computers are build with switches ons and offs so you can esaly implement binary ) ,this doesnt mean that its not possible to develop a different thecnology that could use the Decimal base 10 , wich its a more powerful
base. Since this base reduces a lot any astronomical calculations.As an example, you mention that a number can be represented by 0s and 1s in binary, so it seems logical that takes more digits and therefor should take more storing space although our present thecnology doesnt allow us to do it in any other way.Well long ago the church stated that earth was flat too because their luck of thecnology.If you take any mathematical funtion like add or divide a number you can esaly see that the process is a lot faster using the decimal base 10 ,more if you try to reduce or classify it.My intuition says that there is a way to use Decimal base 10 in a computer, you only need that a computer could think like a human.Best Regards
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Tuesday, August 21, 2012 at 8:44 PM
@Mark Base 10 was optimized for efficiency for humans. That's why they teach it in schools, and why we use it daily.

Thing is, there is nothing inherently "better" about base 10 -- you can perform calculations in any base, it's just harder for a human to use different bases since they're not intuitive.

Base-10 computers are possible but they require technology that provides 10 distinct quantum states. Currently most computers use binary because it's easy to provide 2 quantum states with a digital circuit. Analog computers have used different bases in the past but they were also far more susceptible to interference.
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Mark
Wednesday, August 22, 2012 at 10:55 AM
Nevertheless, I dont agree with this statement :"Thing is, there is nothing inherently "better" about base 10 -- you can perform calculations in any base, it's just harder for a human to use different bases since they're not intuitive.",here Im afraid that you have to prove it, mathematically speaking.And I can prove it with a simple problem: Try to classify a number with "x" digits using a mathematical operation so the result can be keep in a constant serial of ordinal numbers.
I believe that using base10 is the best option to do this even more exact than base 12 known to be as best base to use.
Best Regards
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Wednesday, August 22, 2012 at 6:39 PM
@Mark Our numeric system is optimized for base 10, which is why you can use "constant serial of ordinal numbers" -- not the other way around. Number bases can be used arbitrarily with no loss of meaning.

Let's say you have twelve cookies. You can write it as:
"I have 12 cookies"
"I have 1100 cookies" (base 2)
"I have C cookies" (base 16, using A-F as additional digits)
"I have 111111111111 cookies" (base 1, count the lines)

Regardless of how you write it, the actual number of cookies in your hand does not change. Therefore the bases are equally good at REPRESENTING the meaning of the numbers.

As for efficiency and speed of calculation... your math skills are optimized towards base 10 because that's the way they taught you (see first point). Binary also SEEMS less efficient at first glance because it takes more digits to write out the numbers ON PAPER, but by that same logic, the most efficient base would be the highest one practical -- if you have 10,000 unique characters usable as "digits", you can then represent every number from 0 to 9,999 using ONLY ONE DIGIT!

A computer, on the other hand, can be built to operate very quickly on many base-2 lines in a digital circuit because it's very easy for it to represent 2 states (on and off) but much more difficult to reliably represent multiple states. In a perfect world it can use multiple voltage levels (i.e. 0V = 0, 1V = 1, 2V = 2...) but this presents 2 challenges.

1) Circuitry for distinguishing these multiple voltage levels is much more complicated to build, and thus more expensive

2) In the real world, circuits are imperfect and are susceptible to noise. TTL circuits for example operate at 5 volts, but signals can vary quite dramatically, so 0 to <1V is defined as "off" and 2-5V is defined as "on". This allows the computer to be far more certain of the results even if voltage fluctuates. In the 10-volt base 10 system, a 5-volt signal (representing 5) can drop down to 3V, and this messes up the calculation because the other chip "sees" a 3 on the line. Possible to build? Yes. Practical for general use? No.

There is certainly a way to make a base-10 computer, at least in theory. A quantum computer does not operate in base 2 because there are multiple distinct states (analogous to "on" and "off", as opposed to "partially on"). This allows it to reliably operate in a higher base.
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Mark
Thursday, August 23, 2012 at 7:39 AM
Thanks for your comments.I would like you to read this article, where there is an interesting work about different bases used in arithmetic and some of their capabilitys to deal with different numbers.
http://www.dozenalsociety.org.uk/basicstuff/osburns.html
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Thursday, August 23, 2012 at 6:43 PM
@Mark That's very interesting, and I agree with it... however, do note that it talks about the ease of manual calculation using the different bases.

It's difficult for a human to deal with 100-digit strings of binary numbers. But for a computer, it's trivial to print more digital logic lines into a microchip &ndash; far easier than trying to build a reliable analog circuit with 10 "distinct" states instead of 2.

Again, this article covers why computers use binary, and in no way implies that binary is universally superior.
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nanda
Wednesday, October 10, 2012 at 10:10 PM
great article..i learnt a lot from the comments too. the cookie example post should be in text books
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Roy
Monday, October 22, 2012 at 9:49 AM
Nookin,
Have you researched Memristors at all? They're a relatively new technology with big implications for computing: they can "remember" any frequency of electrical charge, meaning it could be used to make a computer that runs on base 10 or larger. Pretty interesting stuff. You should look it up. Thanks for this article, very helpful and concise!
-Roy
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cj
Sunday, November 25, 2012 at 5:26 PM
awesome article. really helped with a project i'm doing for school.
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Napolean
Monday, November 26, 2012 at 6:50 PM
Assuming the problem with a base 10 computer is data corruption (excluding complexity of developing a base 10 computer), couldn't we simply use some type of check sum or hash algorithm to verify the data's integrity?

Even with the additional load of calculating the check sum, one could imagine that the increased efficiency would more than make up for the additional calculations.
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Monday, November 26, 2012 at 7:51 PM
@Napolean The problem with a base-10 computer isn't data corruption per se -- it's a problem with an analog 10-bit computer that has, say, 10 voltage levels. A checksum algorithm, it would need to be implemented using the same presumably corrupt base-10 analog logic. See the problem there? :P

A true 10-bit computer would need to be made up of components that have 10 distinct, unambiguous states &ndash; something akin to quantum states of an electron (hence the term "quantum computer"). Such a computer will not be subject to data corruption in the way that an analog one will be.

There are also other costs involved. If it costs X units to produce a 1-bit (binary) circuit element and 10X units to produce a 1-dit (decimal) circuit element, it will be possible to build a 10-bit circuit that's capable of holding 1024 possible values for the same price as a "more efficient" decimal circuit that can only hold 10 possible values. Thus the binary computer is actually more "efficient" for a given price point.

@Roy Memristors are still analog devices &ndash; they're quite fascinating, but from what I know, they have the potential for improving computers by reducing the size of a memory element (which currently requires a much more complicated circuit) but it would still be a 2-state device (has resistance vs. doesn't have resistance). Attempting to define "states" of resistance will result in the same problems that plague analog computers in general.
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Monday, November 26, 2012 at 9:14 PM
Nookkin, do you know about mitochondria being networked nanoscale tunneling electronic devices? They can gate electrons at four or five different electric potentials between 500 millivolts and around 1.3 volts. These mitochondria in all the living cells on earth all have electron flow pretty much like the electron flow in doped semiconductors. To handle all the computation involved in managing the five thousand or ten thousand chemical reactions taking place in a living cell, it would make a lot of sense for these guys to be the intracellular quantum computer. You can watch them doing their electron flow, but it's a little bit like watching a brain's fMRI: You know that something's happening but you don't know what it is (as Bob Dylan pointed out a long time ago). Electron flow in networked mitochondria is not some theory, either --- it's a biophysically measurable phenomenon. If those electrons weren't flowin' in your mitochondria right now, you would NOT be reading this.

(I know, mitochondria are supposedly onlhy good for making ATP from ADP by pumping protons --- the opposite of electron flow. Some guy got a Nobel prize for saying that! If that's true, then a Toshiba is a not very good space heater.)
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Sashko
Thursday, November 29, 2012 at 7:42 AM
Nookkin, thank you very much for the article and the comments. I have understood very well about why computers use binary base.
I have a question about the binary base in general.
I know it is a bit off-topic, but you seem to understand numbers well, so I hope you answer.

I find it misleading about the binary and any other base, how it treats Zero.
Zero represents "nothing", but the way it is used, it doesn't represent "nothing", but is just used as another symbol.

Here is an example is binary base.
0 is nothing.
1000 is |||||||| or 8 in decimal base. Here 0 is not nothing and could be replaced with any other symbol, for example, @.
So
1@@@ will also be equal to |||||||| or 8 in decimal base.

My point is that, thought it is called binary there are actually 3 symbols.
"0" to represent "nothing"
"1" to represent "one"
"0" to represent the idea of "position" in numbers.

Why do you think it was called binary though? It applies to other bases as well.

Thank you!
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Thursday, November 29, 2012 at 5:58 PM
@Sashko It's called "binary" because there are 2 symbols, 0 and 1.

Note that binary, or any other number system for that matter, is simply a way to represent numbers, so the symbol "0" doesn't mean anything by itself.

A representation of a number consists of an infinite number of "place values" starting with the units (1). Each place value has a numeric value equal to the base raised to the place value's position. With this in mind, the 0 simply indicates "the number doesn't contain anything from this place value" -- we write in the zeros to make sure the actual place values don't get shifted over.

You can write the number 5 in binary in 3 different ways:
101
0101
000000000000000000000000000000101

They still represent the exact same number.
101 = 1*(2^2) + 0*(2^1) + 1*(2^0) = 5
0101 = 0*(2^3) + 1*(2^2) + 0*(2^1) + 1*(2^0) = 5
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Sashko
Thursday, November 29, 2012 at 8:21 PM
@nookkin Your explanation makes sense.
Thank you!
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Sashko
Thursday, November 29, 2012 at 9:42 PM
I just kept reading on the topic. And have found an article on Zero.
http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Zero.html
Maybe it will be interesting for others as well.
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Jiyk Pee
Monday, January 28, 2013 at 10:29 AM
Can you tell me why we program in binary number system
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Monday, January 28, 2013 at 1:37 PM
@Jiyk Pee We don't program in the binary number system. Computers just happen to store our programs in a certain way, in this case using 32 (or 64) bits for each instruction word.
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Aaron Stone
Tuesday, February 26, 2013 at 10:40 PM
@Ben
Actaully it could not have more than one current. They would have to translate back to a binary sort of system to unify them, or else they will all have to connect.
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Ben
Wednesday, February 27, 2013 at 7:50 AM
What Roy said about memsistors got me going on a different tangent of QC's. what If, instead of making different VOLTAGES for each quantum state, we did something else, like different electrical FREQUENCYS. Say state 1 is 5v but at 60 Hz, state 2 could be 5v 75 Hz, state 3 5v 90 Hz and so on. This still has a wide tolerance, as we could make the gaps wider or narrower depending on the use (smaller gaps for in laboratories, larger for a home desktop).
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Bhushan
Thursday, May 30, 2013 at 2:56 PM
Nice explanation , is it possible to learn binary language ??
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Ben
Thursday, May 30, 2013 at 5:03 PM
In a way yes, but binary itself isn't a language. In order to convert binary to words, you have to use some sort of encoding, with the most common of which are ASCII and UTF-8. With ASCII each byte (group of 8 bits, or binary characters) corresponds to a character. For example, if i have 01111000, in ASCII I would find what ASCII translation that is, which in this case is "x" (little x, big X is 01011000). In UTF-8 "x" is the same, but there are some additional characters and the mapping could be different.
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Sohaib Jamil
Saturday, June 8, 2013 at 12:04 PM
I understand your article but i have a problem if binary use large space then decimal then why still computer process in binary ???? Any group or lab working on switches that hold 10 different states ????

thanks a lot

@KK Sohaib
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Saturday, June 8, 2013 at 12:12 PM
@Sohaib Jamil While binary does use more "space" (i.e. wires/switches) than decimal, it's still quite easy to make billions of those connections on a chip. Building switches that hold 10 discrete states is possible but unless and until it becomes practical to manufacture them, it will be much cheaper and more efficient to keep using binary. Not sure of any specific examples though.
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Milo
Saturday, July 6, 2013 at 7:06 AM
Nookkin,
I'm following right along with your comments about binary versus any other set. I understand the 'on'/'off' and present/not present and the reliability of such. So I understand why we are currently using binary. From your comments I see why what I wonder about will be difficult and likely some time off. But I would like your thoughts on this.

With my limited knowledge of the human brain and it's structure, I understand that within the brain one node (bit in computer terminology) can have one or several connecting nodes. Depending on the synapes (voltage if using computer terminology) none, one, all, or any combination could be "opened".

It seems to me, that even though it is not difficult to quickly pass through many bits of data, it would still be quicker to pass through fewer. Also, the brain may store some data regarding the position in the string such that the same node can be used in several data strings.

I'm not sure about how one would manage such a system, but based on what you know, would it be possible one day to structure a processor to use the same bit in multiple data strings? What about less nodes and more connections? This would relate to the binary versus other bases.

I wonder if the human brain uses a numbering (naming) system of 10,000 symbols (pick whatever number you wish)such that one node is required for each symbol. Thus one full thought can be done with only a few nodes. For computers to become even smaller and faster, it may take a completely different architecture then the long stings of 0 and 1 that we currently use.

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jgwr5
Thursday, July 25, 2013 at 4:10 AM
@kenoly infinitely variable states using biological fluidity is preferable for hardware, recommending spherical rather than linear math. Quanta are not as great a leap forward.
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Thursday, July 25, 2013 at 2:02 PM
what biological hardware do you have in mind for your biological fluidity? Are you aware of electron flow in mitochondria --- gated, networked, nanoscale, electronic, and having four or five electric potentials =eight or so states? But if you know of some other biological candidate, I'd really like to hear what it is.
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vicky
Friday, July 26, 2013 at 2:51 PM
hey em complete techy but em ntt really in to hw does computer process or understand i mean hw does it do hw does it process where does it get through intelligence of understanding of on and off switch thing can any body plz help here ...
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vicky
Friday, July 26, 2013 at 2:53 PM
where does it get intelligence of understanding on and off switch thing or binary codes help here appreciated
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Friday, July 26, 2013 at 8:19 PM
@vicky A computer has no intelligence and doesn't "understand" anything. It's just a dumb machine that patiently follows a bunch of instructions... billions of them every second. It's entirely up to the (human) programmers to make it do something useful.
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Robert Salmond
Thursday, August 29, 2013 at 11:09 PM
Good article Nookkin, but I do have to disagree with some of the points, especially about the limitations of circuitry...

I have been working out ways to achieve decimal computation, using standard electrical circuitry, for many years now. Not only do I believe that it very possible, but that it should be pursued as soon as possible to help usher in the age of quantum computation and to relieve internet data congestion currently.

For starters, it is a bit of a leftover myth that electrical circuits would not be able to properly distinguish ten states of voltage (amplitude). An Analog to Digital Converter (A/D or D/A) already does this with startling precision. Your computer microphone sends a constantly fluctuating state of voltage (amplitude) into the D/A as an analog signal. The D/A then discerns and carefully calculates the voltage of the wave at any given point (depending on the sample rate) and converts that value into a binary string. Modern D/A's are extremely accurate and reliable; this is why the Music, Film and Measurement industries are able to use them professionally... It is also why I can use my computer as a legitimate and accurate oscilloscope.

I do agree that a decimal processing computer would, in fact, use far more space and circuitry, but this is no longer a problem thanks to the miniaturization of electronics. When I got my first desktop computer, the case had very little free space inside of it. However, that has changed dramatically and now my case is almost all free space (making me wonder why cases have not really changed size from the standard ATX form factor). The Smart Phone and tablet further this miniaturization. So, when base-10 computing was last given any real consideration by the industry, the size of it was impossible, but now, a base-10 computer would probably just fill my case the way a binary system used to.

Now, some are looking forward to quantum computing as the next leap, and I am on board and excited for this to happen, but it's not around the corner as many hope. The problem with this is that it may still take another decade or two to actually build the quantum base-10 computer circuits that make this possible, but it will also still take another decade or two for software and ancillary hardware developers to do their part once they actually have the hardware to develop with. Because this is such a monumental leap in the very foundations of how things will be processed, it will require re-writing everything... You won't be able to just install a binary version of Windows or Linux on it without an emulator, and even if you did use an emulator, you would lose all the benefit of operating in base-10... So, the only way to prepare for that is with a hybrid technology that gets developers developing in base-10 as soon as possible. If programmers and developers had already written and worked out the foundations for base-10 computing on a standard electrical processor by the time the quantum computer was released, it would only take a few years to adapt it for this as opposed to whole decades otherwise, meaning that we could have a quantum computer on our computer desk much sooner.

I have designed a number of crude concepts to make base-10 possible with standard electronics, including a design for a 10-state transistor (a decistor?) that would be at the core of switching for this computer depending on the state of voltage given to it (Two inputs , Nine [actually nine because zero would need no output] outputs). If this design works, it means that you could send one signal into it (from 0vdc to 9vdc +/- .05vdc) and work with each of the nine outputs discreetly (If signal is a 5, than activate the part of the circuit designed to to react to 5). This means that each input pin of a base-10 processor (loaded with decistors and transistors) could take any input between 0 and 9, process it, and spit out a result on the output pins that is again 0 to 9. While there may be various degrees of logical binary operators between the decistors, it would still flip flop a single cycle in base-10. The advantages would be almost immeasurable... I've got most of this base-10 computer sort of figured out, but I am still stuck on finding an efficient way to store the values in a single memory cell without having to use 9 capacitors...

Either way, interesting article and discussion worth having and seeking solutions to, in my opinion... Feel free to email me for further discussion.
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Zxen
Wednesday, September 18, 2013 at 1:28 PM
That's not all there is to it. Binary is stupid and inappropriate. We only use it because wires were thick and having ten wires through ten switches per tens column (naughts, tens, hundreds, thousands etc columns) would have taken up more space. Now that wires are thinner, a base ten computer system is easy to create, and these ridiculous translations into this stupid binary number system that relates more to The Penguin than humans (he only had two fingers on each hand) are completely outdated and should be abandoned so nobody ever needs to waste years mastering it when they could get busy creating.

In binary switches, you have ONE wire from ONE switch. With 8 switches you can achieve 255 (128+64+32+16+8+4+2+1).

In base ten switches, you would maybe need 255 wires and switches OR you could pulse the electricity so quickly or in some kind of pattern that you would only need ONE switch OR you could control the STRENGTH of the current so that the computer knows precisely which number you mean.

MY LIGHT SWITCH AT HOME HAS AT LEAST 1 MILLION SETTINGS USING AN ANALOGUE DIMMER. IT IS NOT SIMPLY OFF AND ON.
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Ganesh
Sunday, November 24, 2013 at 6:35 AM
When computer uses binary number system. why binary number system is suitable for computer rather than other number system i need a good example . i am confused

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chandan
Wednesday, September 17, 2014 at 12:41 AM
Explain why binary digits are used to code data to be stored in computee?
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Katie
Tuesday, January 27, 2015 at 10:30 PM
Huh, that makes so much more sense now. Cool!
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Bosgraaf
Wednesday, January 28, 2015 at 5:36 AM
Nice explanation, a good read to learn about binary and its references with other mathematical configurations.

Binary originates from a time where classical science got implemented to create a simple code for the on and off state of a current.
on = 1
off = 0

Our numerical system originates from a time where we started to count on our fingers, with 10 being the highest.
We have 10 fingers and somewhere in our history we determined the iconology of zero to be 0.

Obviously this makes logic sence from a humane perspective, yet i can also imagine it to be somewhat counterintuitive.... but only from a iconology and symbology perspective.

With rapid developments in quantum coding, i am curious if we would decide to keep binary as a standard for these task.... or would we perhaps decide to create a more "universal" and easyer aproach.
For example:

on: -
off: |
both: /

I know that i would find it intuitive.
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Iconoclast
Friday, February 27, 2015 at 7:40 AM
I found very, very interesting the comment by Robert Salmond. There is another advantage in using bases bigger than base two: The less the needed digits to represent a quantity, the lesser the frequency of the clock, and therefore the lesser the problems with electromagnetic noise. Base ten would offer the additional advantage of being compatible with human universal intuitive way of calculating. I'd like to talk to Mr, Salmond to further discuss the theme.
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Ayub Sherif
Friday, April 10, 2015 at 11:15 AM
I was looking for a way to simplify why computers use binary for a beginner, and your explanation is perfectly useful. I will give 10/10 for the simple and sufficient info.
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Erastus Gitaka Kiyo
Sunday, May 3, 2015 at 5:23 AM
@nookkin
How would a high school student reply to the following question?

State three reasons why computers use the binary system to represent data (3 marks)
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Kyra
Sunday, October 18, 2015 at 8:53 AM
WOW loved this article! Amazingly explained, this has helped me with my uni work!
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Kyra
Sunday, October 18, 2015 at 8:54 AM
WOW loved this article! Amazingly explained, this has helped me with my uni work!
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JS
Saturday, November 14, 2015 at 11:53 PM
@ @ "because binary is actually 2 states of the computer. "On" or "off". the computer KNOWS that there is either electricity flowing through a component, or there is not." If there is an entity that "knows" or is structured to recognize the signature that it is given. Wouldn't it stand to reason that merely an act of creating another signature for it to recognize other than on / off; I guess what I'm asking is, can we get away from the linear approach to transferring data?
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Sunday, November 15, 2015 at 10:40 AM
@JS We certainly can! The issue is that when it comes to electricity, there are only 2 discrete states ("on" and "off"). A TTL chip can accept somewhere between 2 and 5 volts as "on", which makes it fairly resilient to voltage changes. If we create, say, a base-10 system using 10 different voltages, the necessary electronics to accurately monitor and maintain the voltage will make it much more expensive to produce. It will also be less resilient to changes since the difference between 2 and 5 volts in this case will be significant (i.e. they're not just the same "on" state).
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orah
Monday, August 29, 2016 at 4:00 AM
I don't have much of a background to comment, but someone above mentioned the scale 0 to 4 to eventually reach a 16 base. On my naive/dummy opinion, why can't we treat it like colors then? All together (1) means white and absence of them (0) means black, but they are also read as a 7 colors scale?
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Monday, August 29, 2016 at 7:06 PM
@orah There's no practical difference in representing a number as a group of digits or as a color (in fact colors on this web page are represented by 3 groups of digits with a scale 0 to 255).

You can also group numbers as needed -- you get base 16 (0-F) by grouping 4 base-1 digits (0-1) and in fact this is used for representing numbers in many programming languages. It's much easier to write "19F" than "000110011111", although they represent the same quantity.

Binary is a fact of circuits -- you either have current flowing or you don't, so there are 2 distinct states. It's very simple to make something that uses binary. If you want a variable 0-4 (say, 0V, 5V, 10V, 15V) it will work but it will be much harder (electrically) to build and will be much more susceptible to noise. A weak 10V signal ("2") might appear as a strong 5V signal ("1") and scramble information easily, whereas in a TTL based (0-5V) binary system, a 2V signal is still seen as a "1".

Likewise you can use quantum states to build a quantum computer which is not binary-based. The key here is that quantum states are distinct -- there's no doubt about the position.
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Friday, March 10, 2017 at 7:07 AM
Don't understand why you're so "locked down" on that "Quantum Computer" thing.

It is very possible to represent more than 2 states with totally normal technology. For starters, representing 3 states instead of 2 is piece of cake -- +5V, 0V, -5V. Done.

Then, you don't need "Quantum Computers" to simply use an analog voltage (say, between 0 and 2.55V) to represent a byte, instead of using 8 bits. Such a computer may not always be totally exact depending on the temperature of the circuit etc., but neither is the brain, and that guy works quite well and certainly has much more power than binary computers!
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Alessio Ventura
Tuesday, February 20, 2018 at 9:41 AM

Todayâ€™s fundamental electronic components can easily represent the presence of potential (i.e., positive voltage) and the absence of potential (i.e., no voltage present). Today the most efficient way to do this is via solid state â€śgatesâ€ť, such as silicon diodes and transistors. In this technology, when potential is applied, a gate will â€śopenâ€ť, allowing current to pass. In the absence of potential, no current passes.

In theory, one can create fundamental components that will pass different voltage amplitiudes, where each amplitude value reresents a different state. 0 continues to represent â€śno potential presentâ€ť and 1 continues to represent â€śpotentialâ€ť, however, now it represents a potential of â€ś1â€ť, as â€ś1 volt stateâ€ť. Extending this, â€ś2â€ť represents the â€ś2 voltâ€ť state, â€ś3â€ť represents the â€ś3 voltâ€ť state, and so on and so forth.

With current solid state physics and components, the cost to build an â€śn-naryâ€ť computer would be quite costly, with the estimated complexity to be AT LEAST Order(nxn), or O(n^2), or â€śn squaredâ€ť, where â€śnâ€ť is the n-nary machine desired. In fact, depending on the design and application, the complexity could reach O(n^n), or n raised to the nth power, simply because every output n of a previous stage can be input to one or more (up to n) of the next n stages.

One solution is to build a â€śVirtual n-naryâ€ť machine that emulates n-nary on 2-nary hardware.
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Katherine
Thursday, March 15, 2018 at 2:03 AM
Iâ€™m not so sure about how to phrase or answer this question: Explain how binary numbers are used in computers.

Would anyone be so kind as to help me with a simple explanation?

Thanks
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Ecelso
Thursday, March 15, 2018 at 8:46 AM
@Katherine
1 - In electronics its easier to differentiate two distant voltages than more values, and so, get more reliability. Circuits use 0V and 5V, meaning 0 or 1, or true or false, yes or no, etc.
2 - Electronic computers use Boolean algebra through logic circuits that admit only two states (https://en.wikipedia.org/wiki/Boolean).
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