What is the number system?
For writing numbers using various methods. They are depicted with the help of symbols represented by different systems. In this article we will understand what the number system is. In fact, this is the way of representing numbers and the rules of action on them that correspond to this method. This system is a sign system. The numbers in it are written with the help of symbols of a certain alphabet, which are called numbers. This is done subject to certain rules.
Writing a number in a certain number system is called a number code. A separate position in the record number is called a digit, and its number - the number of discharge. Digit is the number of digits in the image number. It coincides with the length of the number.
Types of number systems
Numbers are represented by non-positional and positional number systems. The nonpositional number system is characterized by the fact that the weight of a digit in it does not depend on the position it occupies in a particular number. An example of such a system is the Roman number system.For example, in the number XXXXV (forty-five), the weight of the digit denoted by X is just 10, regardless of position.
Next, we will understand what is the positional number system and how is it different from the non-positional number system. In the positional number system, the weight of any digit will vary depending on what position it will occupy in the sequence of digits that depicts this number. The main advantages of any positional number system are:
- limited number of characters used to represent numbers;
- ease of performing arithmetic operations.
The main characteristic of a positional system is its foundation. Consider what is the base of the number system. The number of different symbols and characters that are used to represent numbers in this system is called the base of the positional number system. Any natural number can be taken as a base. Therefore, the positioning systems can be infinite. Binary, decimal, hexadecimal, etc. number systems are all examples of positional number systems.
What is the decimal number system
The decimal system is now generally accepted number system. Decimal, it is called, because in it ten units of the lower category are one unit of the higher category. The number 10, respectively, is the basis of the decimal number system.
To write numbers in it, use the following ten numbers: 0, 1, 2, 3, etc. The ranks in it have their own names: hundreds, tens, units. Every 3 categories are combined into a class: a class of millions, a class of thousands, a class of units. When reading numbers, use class names.
Its value depends on the digit in which the digit is located. For example, the number 7537 consists of 7 thousand, 5 hundred, 3 dozen and 7 units. In this case, the first number seven will indicate the number of thousands, and the last one means the number of units. If a digit moves one digit to the left, then its value increases 10 times, and if it moves to the right, it decreases 10 times.
What is a binary number system
The basis of the computer is a binary number system, in which two digits are used - 0 and 1. A computer has two stable states: there is current or no current; high voltage or low; magnetized or not magnetized. One state will correspond to a value equal to one, the second - to zero.The advantages of the binary number system are as follows:
- Elements with 2 possible states, and not several, are suitable for its realization.
- Presentation of information using only two states is robust and reliable.
- The algebra of logic can be used to perform transformations.
- And finally, binary arithmetic is simpler than decimal.
All this leads to the simplification of the transfer, processing and storage of information on a computer. The most significant disadvantage of the binary number system is the rapid increase in the number of digits.