Numerical systems


Just as the first forms of writing appeared long after the development of speech, the first efforts to create a graphical representation of numbers came long after people learned to count. Probably the oldest way of keeping track of a count was by means of a counting system that included the use of a series of physical objects such as pebbles or sticks . Judging from the habits of current indigenous peoples, as well as the earliest finds from written or sculpted records, the earliest numbers were simple and stick- shaped ,marks or marks on one or a piece of ceramic . Having no fixed units of measurement, no coins, and no trade beyond barter, people had no need for written numbers until the beginning of so-called historical times .


What are number systems?

The number systems are a set of rules , norms and conventions we allow a representation of all natural numbers , by a large group of symbols basic and is defined by the database you use.

  • What are number systems for?
  • Characteristics of number systems
  • Source
  • History
  • Types of number systems
  • Application of number systems
  • Operations
  • Importance
  • Examples

What are number systems for?

The main objective of number systems is to count the different elements that a set has . Through them we can get to build all valid numbers within the number system . Its purpose is to represent numbers.


Characteristics of number systems

Among the main characteristics we can mention the following:

  • Each number system is characterized by its base.
  • Number systems have a base or set of symbols that allow representing different numerical quantities.
  • They have a figure or quantity that is formed by the juxtaposition of the different elements.
  • Each element within the number system has a weighted value.
  • The number 0 expresses or denotes the absence of a certain quantity.
  • It is a positional system.
  • They are made up of digits.


To discover the origin of the numbers we must transport ourselves to the Egyptians who were the first inhabitants of the earth who had a decimal system , known at that time as the hieratic number system .


Since ancient times, man has seen the need to count things to achieve proper control . This was one of the main reasons why men devised a system of numbering . Throughout history , base 10 was the most used, however there was also the Babylonian numbering that used a range between 10 and 60, and the Mayans, who used numbers between 20 and 5. About 5000 years ago civilizations began to count and use the units , hundreds , tens, etc., varying the way of writing the numbers. The oldest numbering systems are Greek, Ionian, Old Slavic, Cyrillic, Hebrew, Arabic, Georgian, etc. The step from manually counting to writing numbers occurred approximately 4000 years before Christ. A rudimentary system of cuneiform symbols was created to represent some numbers that were later adopted by the Sumerians of Lower Mesopotamia , who were responsible for creating the oldest numerical figures in history. The birth of Egyptian numbering it was based on the repetition of symbols and their succession in ascending or descending order and had a base 10, tens, hundreds, thousands.

Types of number systems

There are two types or two major classifications of number systems:

  • Positional : it is the type of numerical system in which the value of a figure changes according to the position in which it is found within the figure of the number. The positional system in turn is subdivided into several types, for example:
    • Binary system : it only has two numerical values, 0 and the number 1.
    • Decimal system : it is the system that has a base 10 and ten digits that go from the number 0 to 9.
    • Hexadecimal system: this system requires 16 different figures to express or represent a number.
    • Octal system : it is the system that has eight figures to express different quantities.
  • Non-positional : This is the number system in which the figure does not depend on the position within the number. For example we can mention the Roman numerals .

Application of number systems

Number systems have the following uses:

  • To count and express the results of a measurement and to perform different calculations.
  • They can be used for encodings of information .
  • They are used in the metric system .
  • They are used in the field of physics to show scalar and derived magnitudes.
  • The octal system is used in computing to group bits.
  • The binary system is also used in computers and electronic devices .


With the number system you can perform arithmetic , addition, subtraction, multiplication and division operations. Each number system has its own way of doing each of these operations.


The number system is of the utmost importance for our daily life because through it we can represent all the numbers and work with them to solve a series of mathematical problems that may arise from day to day. It is important in the field of computation , electrical and metric , for the realization of measurements.


  • Binary System: 0, 1
  • Decimal System: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
  • Hexadecimal System: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

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