The most popular number systems

The number system is a special way of writing numbers using a specific set of digits - special characters. This set of numbers represents a sort of alphabet, through which a person can read the recorded number.

In the process of the development of civilization, there arose a lot of systems for writing numbers. At first these were primitive circles, sticks or hooks, the number of which was equal to the number of counted objects. As figures, letters of the alphabet, and even syllables of speech could act. Ultimately, all past and current number systems can be divided into three groups: positional systems, non-position and mixed ones.

In non-position systems, the weight and significance of the figure does not directly depend on the position occupied in the number. In this case, certain restrictions are imposed on the order of the digits, their location in increasing and decreasing order. For example, all known Roman numerals are a non-position number system.

If in the system the weight of the digit changes directly depending on the place in the sequence to which this number is written, then the system is considered positional. For example, the number 888 is written in the same numbers, but they have different quantitative value depending on the place occupied: 8 hundreds, 8 tens, 8 units.

Any positioning system is characterized by its base. In a positioning system, the base is the number of different characters or characters that are used to write numbers in the system. Any natural number can be used as a basis . Thus, it is possible to construct an infinite set of different positional systems. Now the decimal system is widely used , binary, octal and hexadecimal. Let's discuss them in more detail.

Decimal system

She came to Europe from India, where she was born not later than the 6th century AD. The system uses 10 digits - from zero to nine. In this case, the information is borne not only by the figure itself, but also by the place on which it stands.

For a decimal system, the number 10 and its degree are particularly important. The extreme number on the right side of the figure represents the number of units, followed by the number of tens, hundreds, thousands, and so on.

The reason for the popularity and prevalence in the world of the decimal number system is that the first human counting machine was his hands. The number of fingers and became the starting point for the account system.

Binary system

In this system, two digits are used - one and zero. The system is built around the number two and its degrees. The rightmost digit denotes the number of units, followed by two, then four, eight, etc.

Using a convenient binary system, any natural number can be written as a sequence of zeros and ones. However, a binary record can encode not only numbers, but also pictures, films, texts, audio recordings. Technically binary coding is implemented quite easily, so it has found wide application in the field of technology.

Octal system

In this number system, eight digits - from zero to seven. In the low order digit 1 means simply one - just like in the decimal system. But in the next digit a unit means 8, then 64 so on. The number 100 written in the octal code is read as a decimal 64.

To convert the octal number 611 to a binary system, you must replace each digit of that number with the corresponding binary triad. And for the reverse translation of a number from binary to octal, it is necessary to select the triads in it from right to left, then replace each three of the digits with the corresponding digit from the octal system.

Hexadecimal System

The number written in the octal system already looks fairly compact. But the hexadecimal system allows you to record even more compactly. From the 1st to the 10th digit in this system, the usual sequence is used - from zero to nine, but the first six letters of the Latin alphabet are used as the next six digits (from 11 to 16) .

As in the previous systems, the number one in the low order denotes unity. In the next rank, it turns into 16 (from the decimal system), and in the next - to 256 (from the decimal system). If the digit F is in the least significant digit, then it denotes the decimal number 1.

Direct and reverse translation from this number system to binary is performed similarly to the above translation for the octal system.