Number System and its types (Decimal, Octal, Hexadecimal and Binary)

The number system is the fundamental part of mathematics. The Number system is an instrument of representing numbers on the number line with the help of a set of symbols and rules. The number system is used to perform any mathematical tasks, may it be the calculation like counting chocolates or toys for nursery kids or the great scientific calculations.

Number is essential for any arithmetic calculation and the measurement of objects. The digit 0- 9 represents the numbers. Number System consists of different types based on the base value of the digits. There are various categories of numbers such as -whole numbers, natural numbers, rational numbers, irrational numbers, real numbers and complex numbers and so on. Like that, there are various types of number systems such as binary number systems, the octal number system, decimal number system and the hexadecimal number system. Here we will discuss different types of number systems. First of all, we must know what the number is.

What is Number?

A number is the symbols which have mathematical value, and are used for counting or measuring objects. Numbers are essential for performing arithmetical calculations. Besides natural numbers, whole numbers, rational and irrational numbers – there are other variations of numbers such as odd numbers and even numbers, prime and composite numbers.

The odd numbers are those which are not divisible by 2 and on the other hand even numbers are those numbers that are divisible by 2. The prime numbers are those numbers which have only two factors and the composite numbers have more than two factors.

In the number system, the numbers are used as digits. 0 and 1 are the most common digits in the number system. They are used to represent binary number systems. The numbers 0 represent the null value. The digits from 0 to 9 are also used for other types of number systems.

What is Number System?

The method of writing the numbers in a system to express the numbers is known as the number system. It is the mathematical method for representing the number by the help of digits or symbols in an arranged manner. It provides a unique representation of each number and also characterizes the arithmetic and algebraic structures. The number systems also allowed us to perform the arithmetic operations like addition, subtraction, multiplication and division.

There are various types of number systems in mathematics. The four most common number system types are:

  • Decimal Number System (base-10)
  • Binary Number System (base-2)
  • Octal Number System (base-8)
  • Hexadecimal Number System (base-16)

1. Decimal Number System (base 10)

Decimal number system uses the ten digits from 0 to 9. In the decimal number system, the positions of the digit successively from the left of the decimal point represent units, tens, hundreds, thousands and so on. This system is presented in decimal numbers.

Every position of the digit shows the particular value of the base. Have an example. 2476 is a decimal number which consists of 6 in units position, 7 in the tens position, 4 in the hundreds position and 2 in the thousands position. The place value of the digits in the decimal system is increased by 10 as 10 is the base of the decimal system. The value of these numbers will be written as:

(2×10³) +(4×10²)+(7×10¹) + (6×1) = (2×1000) + (4×100) + (7×10) +(6×1)

2. Binary Number System (base 2)

This system has only two base numbers. The two binary digits are 0 and 1. The figures described under the binary system are known as binary numbers. These numbers are the combination of only two digits, I.e., 0 and 1. Using this number system, the Least Significant Bit (LSB) is 0 and the Most Significant Bit (MSB) is 1. Binary number system supports Arithmetic Operations like addition, subtraction, multiplication and division. 11011 is a binary number. The binary numbers can be converted to any other number system.

3. Octal Number System (base 8)

In this type of number system, the base is 8. It uses the number from 0 to 7. This type of number is generally used in computer applications. Octal numbers can be converted into decimal systems and the decimal numbers can easily be converted into octal number systems.

4. Hexadecimal Number System (base 16)

In the hexadecimal system, the number is represented with the base of 16. The numbers first represented in the hexadecimal system are like in the decimal system, that is 0 to 9. Then the numbers are represented with the alphabet from A to F. Example of a hexadecimal number is 0xE9B5.

So, here we discussed different types of number systems. All the number systems can be converted to the other number system. To know more about the number systems and any other mathematical topic download Cuemath app.