Table of Contents

- 1 Number System:
- 1.1 Data:
- 1.2 Conversion Of Number System:
- 1.2.1 1. Decimal To Binary Conversion:
- 1.2.2 2. Decimal To Octal Conversion:
- 1.2.3 3. Decimal To Hexadecimal Conversion:
- 1.2.4 4. Binary To Decimal Conversion:
- 1.2.5 5. Binary To Octal Conversion:
- 1.2.6 6. Octal To Decimal Conversion:
- 1.2.7 7. Octal To Binary Conversion:
- 1.2.8 8. Hexadecimal To Decimal Conversion:
- 1.2.9 9. Hexadecimal To Binary Conversion:

**Number System:**

The number system is defined with a different format like decimal octal binary etc. The system uses the binary system to manage the user instruction and generate output.

**1. Positional Number System:**

The numeric value manages the base of positional value. The position of a digit indicates the significance to be attached to that digit. This system has radix base or base to control the data and its processing.

**2. Binary Number System:**

It is a number system that represents only 0 or 1 and radix is 2.

**3. Decimal Number System:**

It is a number system that represents 0 to 9 and the radix or base is 10.

**4. Octal Number System:**

It is a number system that is represented between 0 to 7 and radix is 8.

**5. Hexadecimal Number System:**

It is a number system that represents between 0 to 9 and A, B, C, D, E, F respectively and radix is 16.

**Data:**

The system uses binary information for processing the data and instruction. The user uses a different type of symbols, numeric value, character, and alphanumeric as input. But the system converts into binary format for data processing. The numbers are defined by its base value that helps to a system for conversion.

**Conversion Of Number System:**

**1. Decimal To Binary Conversion:**

In this conversion method, we divide a number by 2 till the quotient is 0. We use remainder value in reverse format for the binary number.

**2. Decimal To Octal Conversion:**

In this conversion method, we divide a number by 8 till the quotient is 0. We use remainder value in reverse format in an octal number.

**3. Decimal To Hexadecimal Conversion:**

- Divide the decimal number by 16. Treat the division as an integer division.
- Write down the remainder (in hexadecimal).
- Divide the result again by 16. Treat the division as an integer division.
- Repeat step 2 and 3 until a result is 0.
- The hex value is the digit sequence of the remainders from the last to first.

**4. Binary To Decimal Conversion:**

- Write down the binary number.
- List the powers of two from right to left.
- Write the digits of the binary number below their corresponding powers.
- Connect the digits in the binary number with their corresponding powers.
- Write down the final value of each power of two.
- Add the final values.
- Write the answer along with its base subscript.

**5. Binary To Octal Conversion:**

In this conversion method, we create the group of 3 digits of binary value from the right or find out its decimal value of each group and combined together octal.

**6. Octal To Decimal Conversion:**

In this conversion method, we use 8^^{0}, 8^^{1},8^^{2} and 8^^{n} than multiply with each digit of the octal number from the right side and find the sum of all digit after processing for decimal value.

**7. Octal To Binary Conversion:**

In this conversion, we find out binary of each digit from octal & represent into 3 bit. Then combine together for binary.

**8. Hexadecimal To Decimal Conversion:**

In this conversion method, we use 16^^{0}, 16^^{1}, 16^^{2 }and 16^^{n} than multiply with each digit of the hexadecimal number from the right side and find some of all digit after processing for decimal value.^{ }

**9. Hexadecimal To Binary Conversion:**

In this conversion method, we can find out binary of each digit from hexadecimal and represent into 4 bit. Then combine together for binary.

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