## Number Systems and Their Explanation Grade XI Note

## Number System:

Any system that is converted in terms of number or symbol or digits is known as number system. Basically there are two types of number system. They are:

1) Positional number system

2) Non-positional number system

## Positional number system:

The number system from which we can further divided in terms of its position that number system is known as positional number system. For example: 1001.

According to positional number system it can further divided into:-

**1) Binary number system**

The number system whose value is 0 and 1 and base is 2 is known as binary number system. For example: (100111)_{2} , (11011)_{2}

**2) Decimal number system**

The number system whose value is 0-9 and base is 10 is known as decimal number system. For example: (1250)_{10} , (1286)_{10
}

**3) Octal number system**

The number system whose value is 0-7 and base is 8 is known as decimal number system. For example: (011754)8 , (201157)8

**4) Hexadecimal number system**

The number system whose value is 0-9 and A-F and base is 16 is known as decimal number system. For example: (10A2B)16 , (1A3B2F)16

**Base or Radix:**

The number contain in number system is known as Base. For example: I binary number system its value is 0 and 1 which base is 2 similarly in decimal number system its base is 10, In octal number system its base is 8, in hexadecimal number system its base is 16.

## Non-positional number system:

The number system from which we cannot further divided in terms of its position that number system is called Non-positional number system. For example: I, II, III, IV

**Complement:**

Computer is unable to perform subtraction like in arithmetic to perform subtraction repetition of addition which is occur is known as complement.

There are two types od complement

**i. r’s**

**ii. r’s – 1**

where r’s = base of number system

In binary number system there are two types of complement. They are 1’s and 2’s complement similarly is decimal number system there are two types of complement 9’s and 10’s.

**1’s complement:**

In binary number system 0 is converted in terms of 1 and 1 is converted in terms of 0 and vice versa is known as 1’s complement. Example: 1’s complement of 100 = 011

**2’s complement:**

In binary number system 1’s complement is added with binary digit of 1 then it is known as 2’s complement. Example: 2’s complement of 100 = 1’s complement of 100 + 1

** 9’s complement:**

In decimal number system each digit is subtracted by 9 of its digit is known as 9’s complement. Example: 9’s complement of 6 = 9-6 similarly 9’s complement of 253 = 999-253

**10’s complement:**

In decimal number system 9’s complement is added with decimal number of 1 then it is known as 10’s complement. Example: 10’s complement of 6 = 9’s complement of 6 + 1