The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

The method of naming or describing numbers is the number system or the numeral system. In algebra, there are all kinds of **number systems**, such as binary, decimal, etc. This tutorial covers the numeral system’s entire definitions with their forms, conversions, and queries.

In mathematics, there are different forms of number systems. The four most prevalent kinds of number system are:

Decimal Machine Number (Base- 10)

System of Binary Numbers (Base- 2)

System of Octal Numbers (Base- 8)

Hexadecimal System of Numbers (Base- 16)

**The system with Decimal Number (Base 10 Number System) **

Base 10 is a decimal number scheme and it uses ten digits, from 0 to 9. In the decimal number system, units, tens, hundreds, thousands, and so on represent the successive positions to the left of the decimal point. In decimal numbers, this system is expressed.

Each location displays a basic power of the base (10). The decimal number 1457, for example, consists of a digit 7 in the position of the units, 5 in the position of the tens, 4 in the position of the hundreds, and 1 in the position of the thousands, the value of which can be written as

(1 x 10^3) + (4 x 10^2) + (5 x 10^1) + (7 x 10^0)

(1 x 1000) + (4 x 100) + (5 x 10) + (7 x 1)

1000 + 400 + 50 + 7

1457

**System of Binary Numbers (Base 2 Number System) **

The base 2 number system is often referred to as the binary number system, in which there are only two binary digits, i.e., 0 and 1. Specifically, a radix of 2 is the standard base-2. The numbers described in this system are referred to as binary numbers, a combination of 0 and 1. 110101, for instance, binary **integers**.

**System of Octal Number (Base 8 Number System) **

The basis is 8 in the octal number system and to represent numbers it uses numbers from 0 to 7. In computer applications, octal numbers are widely used. It is the same as the decimal conversion to convert an octal number to a decimal.

**The method with Hexadecimal Number (Base 16 Number System) **

Numbers are written or represented in the hexadecimal system using base 16. The numbers are first represented in the hex system, much as in the decimal system, i.e. 0 to 9. Then, using the alphabets of A to F, the numbers are represented.

**Hexadecimal0123456789ABCDEFDecimal0123456789101112131415**

When we type any letter or word, since computers can only understand** rational numbers **and **irrational numbers**, the computer translates them into** real numbers**. Only a few symbols called digits can be understood by a computer and these symbols describe distinct values depending on the position they hold in the number. The binary number scheme is, in general, used in computers. The octal, decimal, and hexadecimal systems are still often used, however.

Numbers can be expressed in all of the divisions of the number system, including binary, decimal, hex, etc. Every number that is expressed in any of the forms of the number system can also easily be translated to another.

In this chapter, we learned about the basics of number systems. We learned about the **properties Of irrational numbers, **types of number systems, and utilizing this base knowledge we can understand the **rationalisation laws of radicals. **These concepts can be utilized to solve mathematical problems.

**1. What are the 4 types of number systems? **

The four most prevalent kinds of number system are:

- Decimal Machine Number (Base- 10)
- System of Binary Numbers (Base- 2)
- System of Octal Numbers (Base-8)
- Hexadecimal System of Numbers (Base- 16)

**2. What are the different types of number systems? **

The four most prevalent kinds of number system are:

- Decimal Machine Number (Base- 10)
- System of Binary Numbers (Base- 2)
- System of Octal Numbers (Base-8)
- Hexadecimal System of Numbers (Base- 16)

**3. What is the highest base number system? **

System of Decimal Number [Base-10]

With the least value being 0 and the greatest value being nine. On the left, the digit or column has the greatest value, while on the right, the digit has the least value.

**4. What is number system with example? **

A system for representing numbers of a certain type (that is, expressing or writing them). Example: There are several systems for the representation of numbers for counting. These include: the usual system of “base ten” or “decimal”:

**5. What is the real number system in math?**

All rational numbers, such as integer-5 and fraction 4/3, and all irrational numbers, such as √2, are included in the real numbers (1.41421356…, the square root of 2, an irrational algebraic number). Transcendental numbers, such as π, are included within the irrationals.

To learn more about **number systems **through simple, interactive, and explanatory visualizations, download the MSVgo app.