People do not just learn to count.Primitive society was guided by a small number of subjects - one or two.All that was more by default to name "a lot."This is considered the beginning of modern calculus.
Brief History
In the development of civilization, people have started to appear the need to share a small set of objects united by common features.Began to emerge relevant concepts, "three", "four" and so on to "seven".However, it was a closed, limited series, the latter concept which continues to carry the meaning of an earlier "a lot."A striking example of this is folklore, come down to us in its original form (for example, saying "Measure twice - cut once").
emergence of complex ways bills
Over time all the processes of life and human activity became more complicated.This led, in turn, to the emergence of a more complex calculation system.At the same time, people used for clarity of expression simplest tools account.They find them around: they were drawing stick on the cave walls with improvised means, do notches laid their interesting number of sticks and stones - these are just a small list of the then existing varieties.In the future, this type of modern scientists were awarded the unique title "unary system of calculation."Its essence is to record numbers using a single type of characters.Today it is the most convenient system that allows you to visually compare the number of objects and characters.The most widely used she received in primary schools (counting sticks).Inheritance "Kameshkovo accounts" can safely assume that modern machines in their various versions.It is interesting and the emergence of the modern word "estimate", whose roots are from the Latin calculus, which is translated not only as "a stone."
score on the fingers
Under extremely meager vocabulary of primitive man gestures often served as an important complement to the information transmitted.The advantage was in their fingers and flexibility in finding a permanent entity that would transmit information.However, there are significant drawbacks: significant limitations and short-term transmission.Therefore, the entire expense of the people who used the "finger method", limited to numbers that are multiples of the number of fingers 5 - is the number of fingers on one hand;10 - on both hands;20 - The total number of the hands and feet.Due to the relatively slow development of this system is the numerical margin lasted quite a long period of time.
first improvements
With the development of the system of calculation and empowerment and needs of humanity maximum number used in the cultures of many nations was 40. Below it was also understood indefinitely (not giving account) number.In Russia, widespread expression "forty times forty".His meaning was limited to the number of items that can not be calculated.The next stage of development - is the emergence of 100. Then began the division into dozens.Subsequently, the number began to appear in 1000, 10,000, and so on, each of which carried a meaning similar to the seven and forty.In today's world the boundaries ultimately be determined.Today introduced a universal concept of "infinity".
integer and fractional numbers
modern numbering system for the least amount of items take one.In most cases it is an indivisible value.However, a more accurate measurement, it is also subject to fragmentation.It is connected with it has appeared at a certain stage of development of the concept of fractional numbers.For example, the Babylonian system of money (balance) was 60 minutes, which was 1 Talanov.In turn, 1 mine was equal to 60 shekels.On the basis of this Babylonian mathematics widely applied sexagesimal crushing.Widely used in Russia shot came to us from the ancient Greeks and Indians.Moreover, these records are identical to the Indian.A slight difference is the absence of the latter stroke.The Greeks top prescribed numerator and the denominator below.Indian spelling fractions received extensive development in Asia and Europe thanks to two scientists: Mohammed Khorezm and Leonardo Fibonacci.The Roman system of calculation equaled 12 units called ounces, to the whole (1 ace), respectively, in all calculations were based on the twelve-shot.Along with the standard is often used and special division.For example, until the XVII century astronomers used the so-called sexagesimal fractions, which were subsequently superseded by a decimal (coined Simon Stevin - a scientist and engineer).As a result of the further progress of mankind has become necessary to further significant expansion of the number series.So there were negative, irrational and complex numbers.The familiar zero is relatively recent.He began to be used in the introduction of modern systems of calculating negative numbers.
use nonpositional alphabet
What is an alphabet?For this calculation system is characterized by the value of numbers does not change their arrangement.Nonpositional alphabet peculiar presence of an unlimited number of items.In terms of systems built on the basis of this type of alphabet, the principle of additive.In other words, the total value is the sum of the number of digits that starts recording.Occurrence nonpositional systems occurred earlier position.Depending on the method of counting the total value of the number is defined as the difference or the sum of all the figures included in the number.
There are disadvantages of such systems.Among the key should be allocated:
- introduction of new figures in the formation of large numbers;
- inability to reflect the negative and fractional numbers;
- complexity of the arithmetical operations.
in the history of mankind used different numbering system.The best known are: Greek, Roman, alphabet, unary, ancient Egyptian, Babylonian.
One of the most common ways to account
Roman numerals, preserved to this day virtually unchanged, is one of the most famous.With her designated different dates, anniversary as well.Also, it has been widely used in literature, science and other areas of life.The Roman system of calculation used by only seven letters of the alphabet, each of which corresponds to a specific number: I = 1;V = 5;X = 10;L = 50;= 100 C;D = 500;M = 1000.
Occurrence
The origin of Roman numerals unclear, history has not kept accurate data of their appearance.This is an undoubted fact: a significant impact on the Roman numbering system of calculation had a fivefold numbers.However, in Latin no mention of it.On this basis, a hypothesis about borrowing the Romans their system from other people (presumably Etruscan).
Features
record of all integers (5000) is made by repeating the above figures.A key feature is the arrangement of characters:
- addition occurs with the proviso that more smaller faces (XI = 11);
- subtraction happens if a smaller figure is facing more (IX = 9);
- the same mark can not be more than three times in a row (for example, 90 recorded cholesterol instead LXXXX).
its disadvantage is the inconvenience of performing arithmetic operations.However, it has existed for a long time and no longer used in Europe as a basic calculation system relatively recently - in the 16th century.
Roman system of calculation is not considered absolutely nonpositional.This is due to the fact that in some cases Subtract smaller figure from larger (eg, IX = 9).
method of counting in ancient Egypt
third millennium BC, is considered the moment of occurrence of system of calculation in ancient Egypt.The gist of it was to record the special characters of numbers 1, 10, 102, 104, 105, 106, 107. All the other numbers are written in the form of a combination of these primitive signs.At the same time, there were limitations - each figure should be repeated no more than nine times.The basis of this method of counting, which modern scholars call "nonpositional decimal system" is a simple principle.Its meaning lies in the fact that the written numbers equals the sum of all the digits of which it was composed.
Unary way to account
Base, which is used when writing numbers one sign - I - called unary.Each subsequent number is obtained by adding a new I to the previous one.The number of I is equal to the value recorded using these numbers.
Octal calculation
This way of counting position, the base of which is the number 8. For a digital display numbers range from 0 to 7. The widespread use of this system has been in production and the use of digital devices.Its main advantage is the easy translation of numbers.These can be converted into the binary system and vice versa.These manipulations are performed by replacing numbers.From octal system are translated into binary triplets (for example, 28 = 0102, 68 = 1102).This method accounts was circulated in the field of computer programming and production.
hexadecimal calculation
Recently in the computer field, this method accounts used actively.At the root of this system is the base - 16 numbering system, which is based on it, is to use the numbers 0 to 9 and the number of letters of the alphabet (A to F), which are used to indicate the range of 1010 to 1510. This method accounts asalready mentioned, it is used in the production of software and documentation related to computers and their components.Based on the properties of this modern computer, the basic unit of which is an 8-bit memory.It is convenient to convert and burn by two hexadecimal digits.The founder of this process was the system of IBM / 360.Documentation for it was first translated in this way.Unicode provides a record of any character in hexadecimal using at least four digits.
Recording Methods
mathematical design method is based on the account you specify it in the lower index in the decimal system.Example, the number 1444 is written as 144410. programming languages to write hexadecimal systems have different syntaxes:
- in C and Java language uses the prefix "0x";
- in Ada and VHDL following standard applies - "1516 # 5A3 #";
- assemblers involve the use of the letter "h", which is placed after the number ("6A2h"), or the prefix "$", which is typical for the AT & amp; T, Motorola, Pascal ("6B2 $");
- also found records such as "# 6A2", a combination of "& amp; h", which is placed before the number ("& amp; h5A3") and others.
Conclusion As we study the system of calculation?Computing - basic discipline within which the accumulation of data, the process of registration in the form convenient for consumption.With the use of special tools is happening registration and transfer of all available information in a programming language.It is then used to create the software and computer documentation.By studying the different systems of calculation, computer science involves the use, as has been said above, the different instruments.Many of them contribute to the implementation of a rapid transfer of numbers.One of these "tools" is a table of calculation systems.Use it quite comfortably.Using these tables, you can, for example, to quickly convert numbers from hex to binary, without possessing scientific expertise.Today, the ability to carry out digital transformation is almost everyone interested in this person because the necessary tools are available to users on public resources.In addition, there are program-line transfer.This greatly simplifies the task of transformation and reduces the number of operations.
