Since ancient times there has been what is called commerce, since even the first inhabitants traded among themselves the sowing, what they collected, the hunting to subsist eating what nature provided them, in addition to making the beginning of a communication.
As man expanded, the stage of discovery came with this, of seeking basic and primary needs, and in the struggle various manifestations began in which he realized that he needed a number system to trade among them.
Whether they had various products from the sea, land or manufactured, it was evident that something was needed to measure, count, write down among many other things and this became a necessity as inventions arrived, including writing and symbols..
Thus was born the numbering system that was established by each civilization according to their customs and knowledge, in addition to responding to the primary needs among the social organization of each one of them using symbols or figures to give rise to the number.
From this numbering system, it was necessary to take into account how all the elements that made it up were going to be organized and for this a base was needed that will consider a number of symbols representing the digits and currently we use the numbering system. 10.
What do you need
- sequence of numbers.
- Infinite.
- signs.
- Letters.
- Base 5 and 100.
- Basis 10.
- Amount.
- Position.
- Additive or multiplicative.
- hybrid.
- Graphic representation.
Instructions
- You already know that a numbering system is based on a set of symbols or figures that are joined together to form quantities that are used to measure, count, operate, among others, with some necessary rules for the result to be effective and exact.
- Likewise, the numeral system needs to have a finite number of figures that can be used in the graphic representation of quantities that go from least to greatest, ranging from five to 10, which are the ones that have been used throughout the history.
- The quantities of numbers that are made with the bases of the numeral systems, whatever they are, have no end, so complete numbers can be made with infinities of digits as in the decimal systems, which many times we cannot even name.
learn step by step
- The base of a numbering system is the main thing to be able to make any number, no matter how large it may be, grouping each digit with others in subsets to improve the possibility of being able to count and that has changed according to the needs of society.
- Mathematical knowledge such as fractions and other operations is the way to learn directly about many economic activities, apart from leading to the use of various applications that have to do with new technologies, demonstrating
- Currently, base 10 is used and many of the ancient civilizations came to use it as well, although there were also others that range from 5 to 100, the way of writing large numbers being very complicated.
- Each numbering system differs from another based on the base it uses to write the quantities, therefore it is necessary to study each one to find out how they used it and if the purpose for which it was invented was achieved.
- According to the base that is taken to carry out a numbering system, it is taken into account that an infinite number of these can be invented according to the needs and it was what was taken during previous times.
- The current system by which all basic and advanced operations are governed is base 10, that is, ten digits, numbers or units and depending on the base used, the numbering system receives its name; example the binary that uses 2 digits in its base.
- Each numbering system defines the use of digits according to its base, an example of this is the one we currently use containing 10 digits ranging from 0 to 9, and in the middle 2, 3, 4, 5, 6, 7 and 8.
- If you invent any system containing numbers in a base, you will get a system that works differently, for example placing a base 15, the digits go from 0 to 14 and so on.
- Each figure has its positional and individual value, so it is important to place a symbol that represents it and this made a difference in antiquity where the number that was included later was unknown.
- So the stripes, points, commas, animals, fingers or hands, among many other shapes, were the numbers of a time when an order was needed to carry out the different measurements and transactions between the members of a nation or between different ones.
- In each of the systems that have a well-defined base, it is necessary to show the placement of the symbols possessed one following the other in order to obtain an exact quantity of what one wants to obtain.
- For this reason, this base will define a specific numbering. Thus, if you have a numbering system where the base tells you that there are four units, logically you should have a symbol for a number that goes from 0 to 4 if you accept 0 as a digit.
- The numbering systems have their nomenclature according to the base, so it is important to be clear about the number of digits with which you work, taking this into account, you should pay attention to the examples that are offered below: Base 10 = decimal, Base 2 = Binary, Base 5 = quinary, Base 100 = hundred, Base 15 hexadiene.
- In addition to all this, in mathematical operations it is necessary to define which base is being worked with, so to identify one from the other it is done with a symbol that identifies this, so if you work with base 10, you have to place it below the last amount number.
- Normally in the base 10 it is not necessary to place it, since it is assumed as a general rule and that we currently work with this numbering system, it is obvious to place that numbering that identifies it, a bit complicated but with practice you learn it.
- In each one of the numbering systems, the base gives the possibility of doing the principles of basic operations and thus the desired amounts are obtained for each one, using of course the signals as appropriate to the civilization. Then we have what we see below.
- Additive or sum. The figures that represent a number are added.
- If a point is worth 5 to get 20, 4 points are placed.
- Subtractive or subtractive. Any symbol that is placed before another has the ability to reduce its value, for example the Romans used letters and if they placed an I before a letter V, IV was obtained, which is the representation of 4.
- multiplicative. Doubling the value of each symbol. For example the lines above the Roman letters that doubled the number to which they led.
- positional. The position determines the value of the symbols, acquiring a greater quantity depending on whether it is further to the right, adding the higher the digit, an example of this can be found when you talk about units, tens and hundreds, taking into consideration the following:
- 532 which would be equal to: 5 hundreds (100) 3 tens (10) and 2 units (1 + 1)
- Therefore, there is also talk of a decomposition of numbers to reach a smaller digit or that cannot be decomposed into a smaller one.
- Among the different numbering systems according to their base, there are the most used, ranging from binary to 16-digit, based on the number of elements depending on their function, so we provide you with a guide so that you can take into account:
- Binary: 2 elements or two digits.
- Tertiary: 3 elements or 3 digits.
- Quaternary: 4 elements or 4 digits.
- Quinary: 5 elements or 5 digits.
- Octal: 8 elements or 8 digits.
- Decimal: 10 elements or 10 digits.
- Hexadecimal: 16 elements or 16 digits.
- Each of the systems has its rule depending on the civilization that used it, as well as having its importance at the right time to be used and it was effective, so there are perfect and exact number systems.
- The important thing is to learn the use of each one and to be able to take advantage of the benefits that mathematics, its signs, operations, symbols, systems, numbers or digits have to be used at any time they are needed.
Tips
- Remember that there are many existing numbering systems today and each one has its way of being identified by the base.
- When we talk about a digit, you should consider that there are many symbols that represent it, but its meaning is for a unitary element.
- Also think that the base of a numbering system is the number of unique elements that represent it, ranging from 2 to an infinite number.
- The numbering system used in today’s society is base 10.
- The decimal number system works with 10 digits ranging from 0 to 9.
- The binary numbering system dealt with digits that go from or to 1, taking into account that they are two digits, nothing more.
With these guidelines you will be able to handle this topic well and improve in mathematics.