How do number system used in computer – Computers rely on various number systems to handle and process data in distinct ways. For instance, the binary number system is employed to store and exchange information within a computer’s memory and between different devices, whereas computer programming often involves the use of the hexadecimal number system.

**What is number system?**

Numbers can be represented or expressed using a technique called the number system. The most widely used number system is the decimal number system, but there are also other popular systems such as binary, octal, and hexadecimal.

**What is the use of number system in computer?**

Number systems are used in computers to represent and manipulate data. The most common number system used in computers is the binary number system, which uses only two digits, 0 and 1, to represent all the numbers. This is because the binary number system is most easily represented in electronic devices, such as transistors, which can be in one of two states (on or off). Other number systems, such as decimal and hexadecimal, are also used in computers to make it easier for humans to read and understand the data.

**Types of Number system**

After addressing the topic of how do number system used in computers, we shall proceed to explore the different classifications of number systems.

So there are mainly 4 types of Number system.

## Binary Number System (Base 2)

A computer can understand only the “on” and “off” state of a switch. These two states are represented by 1 and 0. The combination of 1 and 0 form binary numbers. These numbers represent various data. As two digits are used to represent numbers, it is called a binary or base 2 number system.

Each binary digit is also called a bit. Binary number system is also positional value system, where each digit has a value expressed in powers of 2.

For example, (101101)2 in decimal is

= 1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20

= 1 x 32 + 0 x 16 + 1 x 8 + 1 x 4 + 0 x 2 + 1 x 1

= 32 + 8 + 4 + 1

= (45)10

In any binary number, the rightmost digit is called **least significant bit (LSB)** and leftmost digit is called **most significant bit (MSB)**.

### Octal Number System (Base 8)

This system uses digits 0 to 7 (i.e. 8 digits) to represent a number and the numbers are as a base of 8.

For example, (24)_{8} in decimal is

= 2×8^{1}+4×8^{0}

= (20)_{10}

### Decimal Number System (Base 10)

In this number system, the digits 0 to 9 represents numbers. As it uses 10 digits to represent a number, it is also called the base 10 number system. Each digit has a value based on its position called place value. The value of the position increases by 10 times as we move from right to left in the number.

For example, the value of 456 is

= 4 x 10^{2} + 5 x 10^{1} + 6 x 10^{0}

= 400 + 50 + 6

### Hexadecimal Number System (Base 16)

In this system, 16 digits used to represent a given number. Thus it is also known as the base 16 number system. Each digit position represents a power of 16. As the base is greater than 10, the number system is supplemented by letters. Following are the hexadecimal symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

To take A, B, C, D, E, and F as part of the number system is conventional and has no logical or deductive reason.

## Conclusion

The number system serves as a written form for expressing numerical values and functions as a mathematical notation to represent numbers. This system follows a place value pattern that extends infinitely in both directions. As we move to the left, the places increase in value, while moving to the right results in decreasing values. Through the use of symbols, we can effectively represent quantities that are infinitely large or infinitesimally small. This intricate structure showcases the captivating harmony within the realm of mathematics.