Binary operation


binary operation

But why is this? I was recently asked this question by someone who knows a good deal about computers. Either way, the answer is quite simple. 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 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, times as big as the other.

There is a fold difference as opposed to a fold difference because is a power of 2 but is not On first glance, it seems like the binary representation of a number uses up more space than its decimal base representation After all, the first is 8 digits long and the second is 3 digits long. The only reason that is "smaller" than 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.

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" through 9. In this system, numbers would be represented in base 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 binary same amount of physical space nanometers as these base-10 switches, the base 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. 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. 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.

Either way, the answer is quite simple What is "digital"? The "on" state is assigned the value "1", while the "off" state is assigned the value "0" The term "binary" implies "two". There is a fold difference as opposed to a fold difference because is a power of 2 but is not Does binary use more operation than decimal? On first glance, it seems like the binary representation of a number uses up more space than its decimal base representation After all, the first is 8 digits long and the second is 3 digits long.

In this system, numbers would be represented in base This is not possible with regular electronic components of today, but it is theoretically possible on a quantum level Is this system more efficient?

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? Yeah, I do wonder how future computers will be. Who would even use a quantum computer? Who will use them? Everybody, much like people use regular transistor-based computers and devices today. Was wondering about this for years. In a 6-state system 0V, 1V, 2V, 3V, 4V, 5V for instance, a simple voltage dip or spike i.

In that case, state v, state v, state v, state v 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. Also, no one has mentioned the different paths idea. Unless they alter the way memory is stored, i. The "different paths" idea still reduces to 2 discrete voltage states, making it expressible using binary.

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. I have to imagine that multi-state switches are what will allow our computing power to continue to increase exponentially. Since the decimal system counted in terms of 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? Two values in the real world imply the use of a 2-valued number system. 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.

My teacher has confused me but thanks to your article I get it now! 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.

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 W operation 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.

These were not merely binary coded decimal. Most machines actually had ten vacuum tubes per digit in each register. 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. Base-10 computers are possible but they require technology that provides 10 distinct quantum states.

Analog computers have used different bases in the past but they were also far more susceptible to interference. 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.

Number bases can be used arbitrarily with no loss of meaning. You can write it as: "I have 12 cookies" "I have cookies" base 2 "I have C cookies" base 16, using A-F operation additional digits "I have 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. 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! In a perfect world it can use multiple voltage levels i. 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.

Practical for general use? 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. 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. You should look it up. Thanks for this article, very helpful and concise! 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.

A checksum algorithm, it would need to be implemented using the same presumably corrupt base-10 analog logic. See the problem there? 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. Thus the binary computer is actually more "efficient" for a given price point. Attempting to define "states" of resistance will result in the same problems that plague analog computers in general.

They can gate electrons at four or five different electric potentials between millivolts and around 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.

Some guy got a Nobel prize for saying that! 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. Here is an example is binary base is nothing 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. Why do you think it was called binary though? It applies to other bases as well. And have found an article on Zero. Computers just happen to store our programs in a certain way, in this case using or bits for each instruction word.

They would have to translate back to a binary sort of system to unify them, or else they will all have to connect. 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.

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 With ASCII each byte group of 8 bits, or binary characters corresponds to a character. For example, if i havein ASCII I would find what ASCII translation that is, which in this case is "x" little x, big X is In UTF-8 "x" is the same, but there are some additional characters and the mapping could be different.

Any group or lab working on switches that hold 10 different states???? 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. 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.

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.

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. Quanta are not as great a leap forward. 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.

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 Binary 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. 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. 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?

If this design works, it means that you could send one signal into it from 0vdc to 9vdc vdc 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 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 The advantages would be almost immeasurable.

Feel free to email me for further discussion. 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 binary 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 In base ten switches, you would maybe need 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. Binary originates from a time where classical science got implemented to create a simple code for the on and off state of a current.

We have 10 fingers and somewhere in our history we determined the iconology of zero to be 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. 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 will give for the simple and sufficient info. Amazingly explained, this has helped me with my uni work! 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. All together means white and absence of them means black, but they are also read as a 7 colors scale? If you want a variable 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 V 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. Click to view a tutorial with various BBCode formatting examples.

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binary operation

Binary Operations - Associative Law

Binary Operations - Associative Law

3 thoughts on “Binary operation”

  1. AndreaBees says:

    Thank you for your podcasts, i subscribe to both twiv and twip and find them both fascinating.

  2. Nysia says:

    Well, said Hardy, there had only been two additions in his lifetime.

  3. AlexandR92 says:

    In the end of this tragedy, King Lear may not be as enlightened as one had thought.

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